From bb02f74d83d5da979edc4896d4b806c1558257b5 Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Sat, 11 Nov 2023 21:01:50 +0000 Subject: [PATCH] build based on 609db08 --- dev/.documenter-siteinfo.json | 1 + dev/allindex/index.html | 2 +- dev/assets/documenter.js | 752 +++++++++++++++--- dev/assets/search.js | 267 ------- dev/assets/themes/documenter-dark.css | 4 +- dev/assets/themes/documenter-light.css | 4 +- dev/assets/themeswap.js | 82 +- dev/assets/warner.js | 87 +- dev/changes/index.html | 4 +- dev/devel/index.html | 2 +- dev/examples/Example001_Solvers/index.html | 4 +- .../Example002_EdgeReaction/index.html | 4 +- dev/examples/Example101_Laplace1D/index.html | 4 +- .../index.html | 4 +- .../index.html | 4 +- .../Example105_NonlinearPoisson1D/index.html | 4 +- .../index.html | 4 +- .../Example107_NonlinearStorage1D/index.html | 4 +- .../index.html | 4 +- .../index.html | 4 +- .../Example120_ThreeRegions1D/index.html | 4 +- .../index.html | 4 +- .../Example125_TestFunctions1D/index.html | 4 +- .../Example150_Impedance1D/index.html | 4 +- .../Example151_Impedance1D/index.html | 4 +- .../index.html | 4 +- dev/examples/Example201_Laplace2D/index.html | 4 +- .../Example203_CoordinateSystems/index.html | 4 +- .../Example204_HagenPoiseuille/index.html | 4 +- .../Example205_StagnationPoint/index.html | 4 +- dev/examples/Example206_JouleHeat/index.html | 4 +- .../Example207_NonlinearPoisson2D/index.html | 4 +- .../index.html | 4 +- .../index.html | 4 +- .../index.html | 4 +- .../Example225_TestFunctions2D/index.html | 4 +- .../Example226_BoundaryIntegral/index.html | 4 +- .../Example230_BoundaryFlux/index.html | 4 +- dev/examples/Example301_Laplace3D/index.html | 4 +- .../index.html | 4 +- .../Example405_GenericOperator/index.html | 4 +- .../Example406_WeirdReaction/index.html | 4 +- .../Example410_ManySpecies/index.html | 4 +- .../index.html | 4 +- .../index.html | 4 +- .../Example422_InterfaceQuantities/index.html | 4 +- .../index.html | 4 +- .../index.html | 4 +- dev/examples/Example510_Mixture/index.html | 4 +- dev/grid/index.html | 2 +- dev/index.html | 2 +- dev/internal/index.html | 46 +- dev/method/index.html | 4 +- dev/misc/index.html | 12 +- dev/nbhtml/api-update.html | 6 +- dev/nbhtml/api-update/index.html | 2 +- dev/nbhtml/flux-reconstruction.html | 6 +- dev/nbhtml/flux-reconstruction/index.html | 2 +- dev/nbhtml/interfaces1d.html | 6 +- dev/nbhtml/interfaces1d/index.html | 2 +- dev/nbhtml/nonlinear-solvers.html | 6 +- dev/nbhtml/nonlinear-solvers/index.html | 2 +- dev/nbhtml/outflow.html | 6 +- dev/nbhtml/outflow/index.html | 2 +- dev/nbhtml/pluto_export.json | 2 +- dev/nbhtml/problemcase.html | 6 +- dev/nbhtml/problemcase/index.html | 2 +- dev/notebooks/index.html | 2 +- dev/physics/index.html | 14 +- dev/post/index.html | 60 +- dev/quantities/index.html | 6 +- dev/runexamples/index.html | 4 +- dev/search/index.html | 2 - dev/solutions/index.html | 32 +- dev/solver/index.html | 18 +- dev/system/index.html | 30 +- 76 files changed, 978 insertions(+), 667 deletions(-) create mode 100644 dev/.documenter-siteinfo.json delete mode 100644 dev/assets/search.js delete mode 100644 dev/search/index.html diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json new file mode 100644 index 000000000..b6cbd5e2b --- /dev/null +++ b/dev/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.9.3","generation_timestamp":"2023-11-11T21:01:21","documenter_version":"1.1.2"}} \ No newline at end of file diff --git a/dev/allindex/index.html b/dev/allindex/index.html index 8df8983e7..067bdd762 100644 --- a/dev/allindex/index.html +++ b/dev/allindex/index.html @@ -1,2 +1,2 @@ -Index · VoronoiFVM.jl
Edit on GitHub

Index

Exported

VoronoiFVM — Module
source

Types and Constructors

Constants

    Methods

    +Index · VoronoiFVM.jl

    Index

    Exported

    VoronoiFVM — Module
    source

    Types and Constructors

    Constants

      Methods

      diff --git a/dev/assets/documenter.js b/dev/assets/documenter.js index 6adfbbbf4..f5311607b 100644 --- a/dev/assets/documenter.js +++ b/dev/assets/documenter.js @@ -1,15 +1,16 @@ // Generated by Documenter.jl requirejs.config({ paths: { - 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia.min', + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', - 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min', - 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/contrib/auto-render.min', - 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', - 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min', - 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/highlight.min', - 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.5.1/languages/julia-repl.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', }, shim: { "highlight-julia": { @@ -70,13 +71,90 @@ $(document).ready(function() { hljs.highlightAll(); }) +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + }) //////////////////////////////////////////////////////////////////////////////// require([], function() { function addCopyButtonCallbacks() { for (const el of document.getElementsByTagName("pre")) { const button = document.createElement("button"); - button.classList.add("copy-button", "fas", "fa-copy"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + el.appendChild(button); const success = function () { @@ -85,7 +163,7 @@ function addCopyButtonCallbacks() { }; const failure = function () { - button.classList.add("error", "fa-times"); + button.classList.add("error", "fa-xmark"); button.classList.remove("fa-copy"); }; @@ -94,7 +172,7 @@ function addCopyButtonCallbacks() { setTimeout(function () { button.classList.add("fa-copy"); - button.classList.remove("success", "fa-check", "fa-times"); + button.classList.remove("success", "fa-check", "fa-xmark"); }, 5000); }); } @@ -138,29 +216,418 @@ require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { // Manages the top navigation bar (hides it when the user starts scrolling down on the // mobile). window.Headroom = Headroom; // work around buggy module loading? -$(document).ready(function() { - $('#documenter .docs-navbar').headroom({ - "tolerance": {"up": 10, "down": 10}, +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, }); +}); + }) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
      Type something to get started!
      + `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
      `; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
      ${count} result(s)
      `; + + search_result_container = ` +
      + ${modal_filters} + ${search_divider} + ${result_count} +
      + ${search_results} +
      +
      + `; + } else { + search_result_container = ` +
      + ${modal_filters} + ${search_divider} +
      0 result(s)
      +
      +
      No result found!
      + `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
      + Filters: + ${str} +
      + `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
      `; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
      +
      ${result.title}
      +
      ${result.category}
      +
      +

      + ${display_result} +

      +
      + ${display_link} +
      +       + ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { // Modal settings dialog -$(document).ready(function() { - var settings = $('#documenter-settings'); - $('#documenter-settings-button').click(function(){ - settings.toggleClass('is-active'); +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); }); // Close the dialog if X is clicked - $('#documenter-settings button.delete').click(function(){ - settings.removeClass('is-active'); + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); }); // Close dialog if ESC is pressed - $(document).keyup(function(e) { - if (e.keyCode == 27) settings.removeClass('is-active'); + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); }); }); @@ -168,151 +635,242 @@ $(document).ready(function() { //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { +let search_modal_header = ` +
      +
      +

      + + + + +

      +
      +
      + +
      +
      +`; + +let initial_search_body = ` +
      Type something to get started!
      +`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
      Type something to get started!
      + `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + // Manages the showing and hiding of the sidebar. -$(document).ready(function() { +$(document).ready(function () { var sidebar = $("#documenter > .docs-sidebar"); - var sidebar_button = $("#documenter-sidebar-button") - sidebar_button.click(function(ev) { + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { ev.preventDefault(); - sidebar.toggleClass('visible'); - if (sidebar.hasClass('visible')) { + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { // Makes sure that the current menu item is visible in the sidebar. $("#documenter .docs-menu a.is-active").focus(); } }); - $("#documenter > .docs-main").bind('click', function(ev) { + $("#documenter > .docs-main").bind("click", function (ev) { if ($(ev.target).is(sidebar_button)) { return; } - if (sidebar.hasClass('visible')) { - sidebar.removeClass('visible'); + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); } }); -}) +}); // Resizes the package name / sitename in the sidebar if it is too wide. // Inspired by: https://github.com/davatron5000/FitText.js -$(document).ready(function() { +$(document).ready(function () { e = $("#documenter .docs-autofit"); function resize() { - var L = parseInt(e.css('max-width'), 10); + var L = parseInt(e.css("max-width"), 10); var L0 = e.width(); - if(L0 > L) { - var h0 = parseInt(e.css('font-size'), 10); - e.css('font-size', L * h0 / L0); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); // TODO: make sure it survives resizes? } } // call once and then register events resize(); $(window).resize(resize); - $(window).on('orientationchange', resize); + $(window).on("orientationchange", resize); }); // Scroll the navigation bar to the currently selected menu item -$(document).ready(function() { +$(document).ready(function () { var sidebar = $("#documenter .docs-menu").get(0); var active = $("#documenter .docs-menu .is-active").get(0); - if(typeof active !== 'undefined') { + if (typeof active !== "undefined") { sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; } -}) +}); }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { -function set_theme(theme) { - var active = null; - var disabled = []; - for (var i = 0; i < document.styleSheets.length; i++) { - var ss = document.styleSheets[i]; - var themename = ss.ownerNode.getAttribute("data-theme-name"); - if(themename === null) continue; // ignore non-theme stylesheets - // Find the active theme - if(themename === theme) active = ss; - else disabled.push(ss); - } - if(active !== null) { - active.disabled = false; - if(active.ownerNode.getAttribute("data-theme-primary") === null) { - document.getElementsByTagName('html')[0].className = "theme--" + theme; - } else { - document.getElementsByTagName('html')[0].className = ""; - } - disabled.forEach(function(ss){ - ss.disabled = true; - }); - } - - // Store the theme in localStorage - if(typeof(window.localStorage) !== "undefined") { - window.localStorage.setItem("documenter-theme", theme); - } else { - console.error("Browser does not support window.localStorage"); - } -} - // Theme picker setup -$(document).ready(function() { +$(document).ready(function () { // onchange callback - $('#documenter-themepicker').change(function themepick_callback(ev){ - var themename = $('#documenter-themepicker option:selected').attr('value'); - set_theme(themename); + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); }); // Make sure that the themepicker displays the correct theme when the theme is retrieved // from localStorage - if(typeof(window.localStorage) !== "undefined") { - var theme = window.localStorage.getItem("documenter-theme"); - if(theme !== null) { - $('#documenter-themepicker option').each(function(i,e) { - e.selected = (e.value === theme); - }) - } else { - $('#documenter-themepicker option').each(function(i,e) { - e.selected = $("html").hasClass(`theme--${e.value}`); - }) + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); } } -}) +}); }) //////////////////////////////////////////////////////////////////////////////// require(['jquery'], function($) { // update the version selector with info from the siteinfo.js and ../versions.js files -$(document).ready(function() { +$(document).ready(function () { // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the // siteinfo.js file, we just return immediately and not display the version selector. - if (typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === 'boolean' && DOCUMENTER_VERSION_SELECTOR_DISABLED) { + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { return; } var version_selector = $("#documenter .docs-version-selector"); var version_selector_select = $("#documenter .docs-version-selector select"); - version_selector_select.change(function(x) { - target_href = version_selector_select.children("option:selected").get(0).value; + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; window.location.href = target_href; }); // add the current version to the selector based on siteinfo.js, but only if the selector is empty - if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) { - var option = $(""); + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); version_selector_select.append(option); } - if (typeof DOC_VERSIONS !== 'undefined') { + if (typeof DOC_VERSIONS !== "undefined") { var existing_versions = version_selector_select.children("option"); - var existing_versions_texts = existing_versions.map(function(i,x){return x.text}); - DOC_VERSIONS.forEach(function(each) { - var version_url = documenterBaseURL + "/../" + each; + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; var existing_id = $.inArray(each, existing_versions_texts); // if not already in the version selector, add it as a new option, // otherwise update the old option with the URL and enable it if (existing_id == -1) { - var option = $(""); + var option = $( + "" + ); version_selector_select.append(option); } else { var option = existing_versions[existing_id]; @@ -326,6 +884,6 @@ $(document).ready(function() { if (version_selector_select.children("option").length > 0) { version_selector.toggleClass("visible"); } -}) +}); }) diff --git a/dev/assets/search.js b/dev/assets/search.js deleted file mode 100644 index c133f7410..000000000 --- a/dev/assets/search.js +++ /dev/null @@ -1,267 +0,0 @@ -// Generated by Documenter.jl -requirejs.config({ - paths: { - 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', - 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', - 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', - } -}); -//////////////////////////////////////////////////////////////////////////////// -require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { - -$(document).ready(function() { - // parseUri 1.2.2 - // (c) Steven Levithan - // MIT License - function parseUri (str) { - var o = parseUri.options, - m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), - uri = {}, - i = 14; - - while (i--) uri[o.key[i]] = m[i] || ""; - - uri[o.q.name] = {}; - uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { - if ($1) uri[o.q.name][$1] = $2; - }); - - return uri; - }; - parseUri.options = { - strictMode: false, - key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], - q: { - name: "queryKey", - parser: /(?:^|&)([^&=]*)=?([^&]*)/g - }, - parser: { - strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, - loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ - } - }; - - $("#search-form").submit(function(e) { - e.preventDefault() - }) - - // list below is the lunr 2.1.3 list minus the intersect with names(Base) - // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) - // ideally we'd just filter the original list but it's not available as a variable - lunr.stopWordFilter = lunr.generateStopWordFilter([ - 'a', - 'able', - 'about', - 'across', - 'after', - 'almost', - 'also', - 'am', - 'among', - 'an', - 'and', - 'are', - 'as', - 'at', - 'be', - 'because', - 'been', - 'but', - 'by', - 'can', - 'cannot', - 'could', - 'dear', - 'did', - 'does', - 'either', - 'ever', - 'every', - 'from', - 'got', - 'had', - 'has', - 'have', - 'he', - 'her', - 'hers', - 'him', - 'his', - 'how', - 'however', - 'i', - 'if', - 'into', - 'it', - 'its', - 'just', - 'least', - 'like', - 'likely', - 'may', - 'me', - 'might', - 'most', - 'must', - 'my', - 'neither', - 'no', - 'nor', - 'not', - 'of', - 'off', - 'often', - 'on', - 'or', - 'other', - 'our', - 'own', - 'rather', - 'said', - 'say', - 'says', - 'she', - 'should', - 'since', - 'so', - 'some', - 'than', - 'that', - 'the', - 'their', - 'them', - 'then', - 'there', - 'these', - 'they', - 'this', - 'tis', - 'to', - 'too', - 'twas', - 'us', - 'wants', - 'was', - 'we', - 'were', - 'what', - 'when', - 'who', - 'whom', - 'why', - 'will', - 'would', - 'yet', - 'you', - 'your' - ]) - - // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" - // would not find anything if searching for "add!", only for the entire qualification - lunr.tokenizer.separator = /[\s\-\.]+/ - - // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names - lunr.trimmer = function (token) { - return token.update(function (s) { - return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') - }) - } - - lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') - lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') - - var index = lunr(function () { - this.ref('location') - this.field('title',{boost: 100}) - this.field('text') - documenterSearchIndex['docs'].forEach(function(e) { - this.add(e) - }, this) - }) - var store = {} - - documenterSearchIndex['docs'].forEach(function(e) { - store[e.location] = {title: e.title, category: e.category, page: e.page} - }) - - $(function(){ - searchresults = $('#documenter-search-results'); - searchinfo = $('#documenter-search-info'); - searchbox = $('#documenter-search-query'); - searchform = $('.docs-search'); - sidebar = $('.docs-sidebar'); - function update_search(querystring) { - tokens = lunr.tokenizer(querystring) - results = index.query(function (q) { - tokens.forEach(function (t) { - q.term(t.toString(), { - fields: ["title"], - boost: 100, - usePipeline: true, - editDistance: 0, - wildcard: lunr.Query.wildcard.NONE - }) - q.term(t.toString(), { - fields: ["title"], - boost: 10, - usePipeline: true, - editDistance: 2, - wildcard: lunr.Query.wildcard.NONE - }) - q.term(t.toString(), { - fields: ["text"], - boost: 1, - usePipeline: true, - editDistance: 0, - wildcard: lunr.Query.wildcard.NONE - }) - }) - }) - searchinfo.text("Number of results: " + results.length) - searchresults.empty() - results.forEach(function(result) { - data = store[result.ref] - link = $(''+data.title+'') - link.attr('href', documenterBaseURL+'/'+result.ref) - if (data.category != "page"){ - cat = $('('+data.category+', '+data.page+')') - } else { - cat = $('('+data.category+')') - } - li = $('
    • ').append(link).append(" ").append(cat) - searchresults.append(li) - }) - } - - function update_search_box() { - querystring = searchbox.val() - update_search(querystring) - } - - searchbox.keyup(_.debounce(update_search_box, 250)) - searchbox.change(update_search_box) - - // Disable enter-key form submission for the searchbox on the search page - // and just re-run search rather than refresh the whole page. - searchform.keypress( - function(event){ - if (event.which == '13') { - if (sidebar.hasClass('visible')) { - sidebar.removeClass('visible'); - } - update_search_box(); - event.preventDefault(); - } - } - ); - - search_query_uri = parseUri(window.location).queryKey["q"] - if(search_query_uri !== undefined) { - search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) - searchbox.val(search_query) - } - update_search_box(); - }) -}) - -}) diff --git a/dev/assets/themes/documenter-dark.css b/dev/assets/themes/documenter-dark.css index c94a294dc..ec054ecc1 100644 --- a/dev/assets/themes/documenter-dark.css +++ b/dev/assets/themes/documenter-dark.css @@ -1,7 +1,7 @@ -@keyframes spinAround{from{transform:rotate(0deg)}to{transform:rotate(359deg)}}html.theme--documenter-dark .tabs,html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable,html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);border-radius:2px;border-right:0;border-top:0;content:" ";display:block;height:0.625em;margin-top:-0.4375em;pointer-events:none;position:absolute;top:50%;transform:rotate(-45deg);transform-origin:center;width:0.625em}html.theme--documenter-dark .admonition:not(:last-child),html.theme--documenter-dark .tabs:not(:last-child),html.theme--documenter-dark .message:not(:last-child),html.theme--documenter-dark .list:not(:last-child),html.theme--documenter-dark .level:not(:last-child),html.theme--documenter-dark .breadcrumb:not(:last-child),html.theme--documenter-dark .highlight:not(:last-child),html.theme--documenter-dark .block:not(:last-child),html.theme--documenter-dark .title:not(:last-child),html.theme--documenter-dark .subtitle:not(:last-child),html.theme--documenter-dark .table-container:not(:last-child),html.theme--documenter-dark .table:not(:last-child),html.theme--documenter-dark .progress:not(:last-child),html.theme--documenter-dark .notification:not(:last-child),html.theme--documenter-dark .content:not(:last-child),html.theme--documenter-dark .box:not(:last-child){margin-bottom:1.5rem}html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-moz-appearance:none;-webkit-appearance:none;background-color:rgba(10,10,10,0.2);border:none;border-radius:290486px;cursor:pointer;pointer-events:auto;display:inline-block;flex-grow:0;flex-shrink:0;font-size:0;height:20px;max-height:20px;max-width:20px;min-height:20px;min-width:20px;outline:none;position:relative;vertical-align:top;width:20px}html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark .delete::before,html.theme--documenter-dark .modal-close::after,html.theme--documenter-dark .delete::after{background-color:#fff;content:"";display:block;left:50%;position:absolute;top:50%;transform:translateX(-50%) translateY(-50%) rotate(45deg);transform-origin:center center}html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark .delete::before{height:2px;width:50%}html.theme--documenter-dark .modal-close::after,html.theme--documenter-dark .delete::after{height:50%;width:2px}html.theme--documenter-dark .modal-close:hover,html.theme--documenter-dark .delete:hover,html.theme--documenter-dark .modal-close:focus,html.theme--documenter-dark .delete:focus{background-color:rgba(10,10,10,0.3)}html.theme--documenter-dark .modal-close:active,html.theme--documenter-dark .delete:active{background-color:rgba(10,10,10,0.4)}html.theme--documenter-dark .is-small.modal-close,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.modal-close,html.theme--documenter-dark .is-small.delete,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.delete{height:16px;max-height:16px;max-width:16px;min-height:16px;min-width:16px;width:16px}html.theme--documenter-dark .is-medium.modal-close,html.theme--documenter-dark .is-medium.delete{height:24px;max-height:24px;max-width:24px;min-height:24px;min-width:24px;width:24px}html.theme--documenter-dark .is-large.modal-close,html.theme--documenter-dark .is-large.delete{height:32px;max-height:32px;max-width:32px;min-height:32px;min-width:32px;width:32px}html.theme--documenter-dark .control.is-loading::after,html.theme--documenter-dark .select.is-loading::after,html.theme--documenter-dark .loader,html.theme--documenter-dark .button.is-loading::after{animation:spinAround 500ms infinite linear;border:2px solid #dbdee0;border-radius:290486px;border-right-color:transparent;border-top-color:transparent;content:"";display:block;height:1em;position:relative;width:1em}html.theme--documenter-dark .hero-video,html.theme--documenter-dark .modal-background,html.theme--documenter-dark .modal,html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:left}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 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.button.is-light.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark 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kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-outlined.is-focused{background-color:#282f2f;border-color:#282f2f;color:#fff}html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after,html.theme--documenter-dark .content 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html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark 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.docstring>section>a.button.is-outlined.is-hovered.docs-sourcelink,html.theme--documenter-dark .button.is-primary.is-outlined:focus,html.theme--documenter-dark .docstring>section>a.button.is-outlined.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-outlined.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-focused.docs-sourcelink{background-color:#375a7f;border-color:#375a7f;color:#fff}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink::after{border-color:transparent transparent #375a7f #375a7f !important}html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after,html.theme--documenter-dark .docstring>section>a.button.is-outlined.is-loading.docs-sourcelink:hover::after,html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark 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.button.is-warning.is-active{background-color:#946e00;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-warning[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning{background-color:#ad8100;border-color:#ad8100;box-shadow:none}html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-inverted:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ad8100}html.theme--documenter-dark .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark 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.button.is-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons 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#documenter .docs-sidebar ul.docs-menu ul.internal{margin:0 0.5rem 0.5rem;border-top:1px solid #5e6d6f}html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li{font-size:.85rem;border-left:none;margin-left:0;margin-top:0.5rem}html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem{width:100%;padding:0}html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before{content:"⚬";margin-right:0.4em}html.theme--documenter-dark #documenter .docs-sidebar form.docs-search{margin:auto;margin-top:0.5rem;margin-bottom:0.5rem}html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input{width:14.4rem}html.theme--documenter-dark #documenter .docs-sidebar #documenter-search-query{color:#868c98;width:14.4rem;box-shadow:inset 0 1px 2px rgba(10,10,10,0.1)}@media screen and (min-width: 1056px){html.theme--documenter-dark #documenter .docs-sidebar 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Gets put into the tag.. function set_theme_from_local_storage() { - // Intialize the theme to null, which means default + // Initialize the theme to null, which means default var theme = null; // If the browser supports the localstorage and is not disabled then try to get the // documenter theme - if(window.localStorage != null) { + if (window.localStorage != null) { // Get the user-picked theme from localStorage. May be `null`, which means the default // theme. - theme = window.localStorage.getItem("documenter-theme"); + theme = window.localStorage.getItem("documenter-theme"); } - // Check if the browser supports user color preference - var darkPreference = false; // Check if the users preference is for dark color scheme - if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { - darkPreference = true; - } + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; // Initialize a few variables for the loop: // // - active: will contain the index of the theme that should be active. Note that there @@ -24,43 +21,64 @@ function set_theme_from_local_storage() { // // - disabled: style sheets that should be disabled (i.e. all the theme style sheets // that are not the currently active theme) - var active = null; var disabled = []; var darkTheme = null; + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; for (var i = 0; i < document.styleSheets.length; i++) { var ss = document.styleSheets[i]; // The tag of each style sheet is expected to have a data-theme-name attribute // which must contain the name of the theme. The names in localStorage much match this. var themename = ss.ownerNode.getAttribute("data-theme-name"); // attribute not set => non-theme stylesheet => ignore - if(themename === null) continue; + if (themename === null) continue; // To distinguish the default (primary) theme, it needs to have the data-theme-primary // attribute set. - var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); - // Check if the theme is primary dark theme - var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); - // If ss is for dark theme then set the value of darkTheme to the name of the theme - if(isDarkTheme) darkTheme = themename; + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } // If we find a matching theme (and it's not the default), we'll set active to non-null - if(themename === theme) active = i; + if (themename === theme) active = i; // Store the style sheets of inactive themes so that we could disable them - if(themename !== theme) disabled.push(ss); + if (themename !== theme) disabled.push(ss); } - if(active !== null) { + var activeTheme = null; + if (active !== null) { // If we did find an active theme, we'll (1) add the theme--$(theme) class to - document.getElementsByTagName('html')[0].className = "theme--" + theme; - // and (2) disable all the other theme stylesheets - disabled.forEach(function(ss){ - ss.disabled = true; - }); + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } } - else if(darkTheme !== null && darkPreference === true) { - // If we did find an active theme, we'll (1) add the theme--$(theme) class to - document.getElementsByTagName('html')[0].className = "theme--" + darkTheme; - // and (2) disable all the other theme stylesheets - disabled.forEach(function(ss){ - if (ss.ownerNode.getAttribute("data-theme-name") !== darkTheme) { - ss.disabled = true; - } - }); + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); } } set_theme_from_local_storage(); diff --git a/dev/assets/warner.js b/dev/assets/warner.js index 5531c8851..3f6f5d008 100644 --- a/dev/assets/warner.js +++ b/dev/assets/warner.js @@ -1,49 +1,52 @@ -function maybeAddWarning () { - // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE - // in siteinfo.js. - // If either of these are undefined something went horribly wrong, so we abort. - if ( - window.DOCUMENTER_NEWEST === undefined || - window.DOCUMENTER_CURRENT_VERSION === undefined || - window.DOCUMENTER_STABLE === undefined - ) { - return - }; +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } - // Current version is not a version number, so we can't tell if it's the newest version. Abort. - if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { - return - }; + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } - // Current version is newest version, so no need to add a warning. - if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { - return - }; + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } - // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. - if (document.body.querySelector('meta[name="robots"]') === null) { - const meta = document.createElement('meta'); - meta.name = 'robots'; - meta.content = 'noindex'; + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; - document.getElementsByTagName('head')[0].appendChild(meta); - }; + document.getElementsByTagName("head")[0].appendChild(meta); + } - const div = document.createElement('div'); - div.classList.add('outdated-warning-overlay'); - const closer = document.createElement('button'); - closer.classList.add('outdated-warning-closer', 'delete'); - closer.addEventListener('click', function () { - document.body.removeChild(div); - }); - const href = window.documenterBaseURL + '/../' + window.DOCUMENTER_STABLE; - div.innerHTML = 'This documentation is not for the latest stable release, but for either the development version or an older release.
      Click here to go to the documentation for the latest stable release.'; - div.appendChild(closer); - document.body.appendChild(div); -}; + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
      Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} -if (document.readyState === 'loading') { - document.addEventListener('DOMContentLoaded', maybeAddWarning); +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); } else { - maybeAddWarning(); -}; + maybeAddWarning(); +} diff --git a/dev/changes/index.html b/dev/changes/index.html index 5b438cbdd..e18eba30c 100644 --- a/dev/changes/index.html +++ b/dev/changes/index.html @@ -1,5 +1,5 @@ -Changes · VoronoiFVM.jl
      Edit on GitHub

      Changes

      v1.13.0 July 24, 2023

      • Add nodevolumes(sys) method

      v1.12.0 July 22, 2023

      • Add functionality for outflow boundary conditions

      v1.11.0 July 17, 2023

      • Add calc_divergences method for checking velocity field divergences
      • Fix form factor calculation and velocity projecion for unstructructured grids and cylindrical symmetry

      v1.10.0 July 11, 2023

      • Use AbstractTransientSolution in gridvisualize stuff

      v1.9.0 June 27, 2023

      • With control.handle_exceptions=true, in case of a failing step, time stepping and embeding now returns the solution calculated so far instead of throwing an error

      v1.8.0 June 20, 2023

      • LinearSolve 2.x

      v1.7.0 May 17, 2023

      • Discrete Sobolev norms

      v1.6.0 May 12, 2023

      • Rework linear solver strategies - prevent combinatorial explosion. E.g. gmres_iluzero is now GMRESIteration(ILUZeroPreconditioner()) etc.

      v1.5.0 May 9, 2023

      • Introduced solver strategies like gmres_iluzero(), direct_umfpack() etc. See documentation of the module VoronoiFVM.SolverStrategies. More to come.
      • edgewise assembly - faster in particular for 3D
      • Plan: edgewise assembly seems to be non-breaking, if this is confirmed, will be made default in 1.6 or (if it appears to be breaking for some) in 2.0.

      v1.4.0 May 3, 2023

      • equation-block preconditioning support with the help of ExtendableSparse.jl

      v1.3.0 April 13, 2023

      • inplace_linsolve! for dense linear system solution in flux functions
      • Mixture flow example 510

      v1.2.0 March 17, 2023

      • Initialization of quantities, create unknowns using Base.map

      v1.1.0 Feb 22, 2023

      • Edge reactions, Joule heating

      v1.0.0 Feb 22, 2023

      • full LinearSolve compatibility

      v0.19.0 Jan 31, 2023

      This is a breaking release. Implementations using default solver settings should continue to work without modifications, albeit possibly showing deprecation and allocation warnings. Really breaking is control of iterative linear solvers and allocation checks.

      Breaking

      • Make solve a method of CommonSolve.solve (and re-export it).
      • Rely on LinearSolve.jl for linear system solution including control of iterative solvers.
      • New verbosity handling. verbose can now be a Bool or a String of flag characters, allowing for control of different output categories. I would love to do this via logging, but there is still a long way to go IMHO
      • Allocation check is active by default with warnings instead of throwing an error. These warnings can be muted by passing a verbose string without 'a'. This is now the only control in this respect. All check_allocs methods/kwargs, control via environment variables have been removed.
      • Deprecation warnings can be switched off by passing a verbose string without 'd'.
      • Improve iteration logging etc., allow for logging of linear iterations ('l' flag character)

      Deprecations

      • Deprecated all VoronoiFVM.solve methods with signatures others than solve(system; kwargs...) which renders them incompatible to the philosophy of `CommonSolve. Updated examples accordingly.
      • Deprecated the following entries of SolverControl/solve kwargs: :tol_absolute => :abstol, :tol_relative => :reltol, :damp => :damp_initial, :damp_grow => :damp_growth :max_iterations => e:maxiters :tol_linear => :reltol_linear :max_lureuse =>
      • NewtonControl

      v0.18.8 - 0.18.10 Dec 11, 2022 - Jan 5, 2023

      • Internal restructuring: remove @create_physics_wrappers macro, reduce boilerplate in assembly, wrap repeating pattenrns into functions. The price in the moment is a bit of a slowdown of assembly.
      • Fix parameter dependency handling (now we can get parameter derivative without solving in dual numbers; see the runh() example in Example430. However in the moment the advantatge is not very clear, so this is on hold...

      v0.18.7 Dec 7, 2022

      • bump gridvisualize compat

      v0.18.6 Dec 3, 2022

      • enable non-diagonal mass matrices for VoronoiFVMDiffEq

      v0.18.5 Nov 30, 2022

      • ready for Julia 1.9, re-enable CI on nighly

      v0.18.4 Nov 29, 2022

      • Add API methods used by VoronoiFVMDiffEq.jl

      v0.18.3 Oct 18 2022

      • Removed some allocations

      v0.18.2 Oct 13 2022

      • Emerging capability of differencing wrt. parameters (experimental, see example 430)
      • Allow iterative methods from Krylov.jl
      • Proper Dirichlet initialization with bcondition
      • Allow for more general matrix structures (banded, tridiagonal, multidiagonal)

      v0.18.1 September 25 2022

      • Working spherical symmetry case

      v0.18 September 12 2022

      • Remove DifferentialEquations interface (move this to a glue package)

      The current method of activating it through require is too brittle with respect to versioning.

      v0.17.1 August 20 2022

      • Fix DifferentialEquations interface, start transition to LinearSolve

      v0.17.0 July 1 2022

      • ensure not to assemble data for species where they are not enabled This change should be breaking only for incorrect code where physics callbacks write into degrees of freedom which are not enabled

      v0.16.5 June 30, 2022

      • add iteration to solver options, allow to choose :cg, :bicgstab.
      • allow setting penalty with boundary_dirichlet!

      v0.16.4 May 25, 2022

      • fix x-t plots

      v0.16.3 March 18, 2022

      • Linearization API
      • relax some type constraints

      v0.16.2 Feb 18, 2022

      • ExtendableGrids 0.9

      v0.16.1 Feb 17, 2022

      • fix quantity postprocessing
      • define unknown access for abstract vectors instead of vectors
      • pass rhs/unknowns wrappers in postprocessing methods
      • integrals as a wrapper type with proper quantity handling

      v0.16.0 Feb 13, 2022

      • Expose ODEProblem (and possibly ODEFunc) from VoronoiFVM.System.
      • Breaking: Remove solve wrapper for DifferentialEquations.solve, instead recommend to call that directly
      • Breaking: Handle DifferentialEquations.jl via Requires.jl.

      v0.15.1 Jan 15, 2022

      • Documentation fixes
      • Fix OrdinaryDiffEq interface
      • added example for current calculation with Quantities
      • Fixed type instabilities in quantities interface

      v0.15.0 Jan 1, 2022

      • Breaking: History is not anymore returned by solve, instead it can be accessed via history after the solution.
      • Cleaned API:
      • OrdinaryDiffEq solver now in CI
      • scalarplot for 1D transient solutions
      • Sparsity detection via Symbolics.jl instead of the sunsetted SparsityDetection.jl

      v0.14.0 Dec 24, 2021

      Backward compatible, hopefully nonbreaking API simplification

      • Boundary conditions are now specified in breaction. Advantages:
        • easy x/t dependency
        • unified (upcoming) interface for parameters
        • unified handling of standard and nonstandard boundary conditions
        • simpler documentation
      • Made NewtonControl alias of SolverControl, continue to work with SolverControl
      • System constructor now directly takes physics callback functions, no need anymore to work with extra physics struct
      • solve() now takes "SolverControl" parameters as kwargs,no need anymore to work with extra NewtonControl/SolverControl struct
      • Notebooks as part of documentation and CI
      • See also the pluto notebook api-update.jl

      v0.13.2 Oct 29, 2021

      • Bernoulli function overhaul

      v0.13.1

      • sorted things with ExtendableGrids
      • nodal flux reconstruction (e.g. for visualization)

      v0.13.0, Oct 13, 2021

      • various bug fixes, explicit numbering of edge nodes

      v0.12.3, July 7, 2021

      • Add quantity id
      • Document quantities

      v0.12.2, July 7, 2021

      Introduce the notion of quantities which can be continuous or discontinuous at interfaces.

      • Quantity handling is implemented on top of species handling
      • Unknowns u and rhs y now passed to callbacks as wrapper types, and can be indexed by quantity or by species numbers. Moreover, this will allow to abstract parameters, gradients etc. in future versions.

      v0.12.0, July 2 2021

      • By default, the u parameter in flux callbacks is now a nspec x 2 array
      • unknowns(edge,u), viewK, viewL are obsolete, they still work for backward compatibility
      • physics.num_species is now meaningless, num_species is automatically detected.
      • SparseSystem and DenseSystem are now type aliases of a parametrized type instead of two independent subtypes of System

      v0.11.8

      • increase chunk size threshold to match argument length in calls to vectormodejacobian

      v0.11.7

      • First attempts on surface flux

      v0.11.1, April 13, 2021

      • Assembly loops cleaned from type instabilities
      • Optionally check for allocations due to type instabilities introduced in physics callbacks. See check_allocs! for more information.

      v0.11, April 12, 2021

      • Depending on Julia 1.5 now
      • Lineaer solvers now based on factorize! from ExtendableSparse 0.5
      • Documentation overhaul
      • Re-checking impedance calculation

      v0.10.13 April 1, 2021

      • Outflow boundary conditions

      v0.10.8 March 22, 2021

      • TransientSolution structure, transient solve
      • Solve compatible with DifferentialEquations.jl

      v0.10.3 Feb 11, 2021

      • Introduce non-mutating solve
      • Optionally record history if log kw is true in solve.

      v0.10.0 Jan 9 2021

      • Moving visualization to the package GridVisualize.jl, emerging from the visualization methods in ExtendableGrids

      v0.9.0 Dec 21 2020

      • Add the possibility to interface with DifferentialEquations.jl
      • Breaking: The API change to passing the unknowns to the an edge callback as a matrix turned out to be a dead end in the strategic sense. In order to extend functionality, we need to be able to pass more data to which we can apply differetiation. Particular plans involve bifurcation parameters and reconstructed gradients. So we return to the viewK/viewL pattern we had before. However, these are now aliases:
        • viewK(edge,u)=unknowns(edge,u,1)
        • viewL(edge,u)=unknowns(edge,u,2)
        In order to ease refactoring in the case where models have been implemented with Matrix access to the unknowns, unknowns(edge,u) returns a matrix of the edge unknowns. For refactoring, just rewrite e.g.
          function flux(y,u,edge)
+Changes · VoronoiFVM.jl
      Changes
      v1.13.0 July 24, 2023
      • Add nodevolumes(sys) method
      v1.12.0 July 22, 2023
      • Add functionality for outflow boundary conditions
      v1.11.0 July 17, 2023
      • Add calc_divergences method for checking velocity field divergences
      • Fix form factor calculation and velocity projecion for unstructructured grids and cylindrical symmetry
      v1.10.0 July 11, 2023
      • Use AbstractTransientSolution in gridvisualize stuff
      v1.9.0 June 27, 2023
      • With control.handle_exceptions=true, in case of a failing step, time stepping and embeding now returns the solution calculated so far instead of throwing an error
      v1.8.0 June 20, 2023
      • LinearSolve 2.x
      v1.7.0 May 17, 2023
      • Discrete Sobolev norms
      v1.6.0 May 12, 2023
      • Rework linear solver strategies - prevent combinatorial explosion.  E.g. gmres_iluzero is now GMRESIteration(ILUZeroPreconditioner()) etc.
      v1.5.0 May 9, 2023
      • Introduced solver strategies like gmres_iluzero(), direct_umfpack() etc. See documentation of the module VoronoiFVM.SolverStrategies. More to come.
      • edgewise assembly - faster in particular for 3D
      • Plan: edgewise assembly seems to be non-breaking,  if this is confirmed, will be made default in 1.6 or (if it appears to be breaking for some) in 2.0.
      v1.4.0 May 3, 2023
      • equation-block preconditioning support with the help of ExtendableSparse.jl
      v1.3.0 April 13, 2023
      • inplace_linsolve! for dense linear system solution in flux functions
      • Mixture flow example 510
      v1.2.0 March 17, 2023
      • Initialization of quantities, create unknowns using Base.map
      v1.1.0 Feb 22, 2023
      • Edge reactions, Joule heating
      v1.0.0 Feb 22, 2023
      • full LinearSolve compatibility
      v0.19.0 Jan 31, 2023
      This is a breaking release. Implementations using default solver settings should continue to work without modifications,  albeit possibly showing  deprecation and  allocation warnings.  Really breaking is control of iterative linear solvers and allocation checks.
      Breaking
      • Make solve a method of CommonSolve.solve (and re-export it). 
      • Rely on LinearSolve.jl for linear system solution including control of iterative solvers.
      • New verbosity handling. verbose can now be a Bool or a String of flag characters, allowing for control of different output categories. I would love to do this via  logging, but there is still a long way to go IMHO 
      • Allocation check is active by default with warnings instead of throwing an error. These warnings can be muted by passing a verbose string without 'a'. This is now the only control in this respect. All check_allocs methods/kwargs, control via environment variables have been removed.
      • Deprecation warnings can be switched off by passing a verbose string without 'd'.
      • Improve iteration logging etc., allow for logging of linear iterations ('l' flag character)
      Deprecations
      • Deprecated all VoronoiFVM.solve methods with signatures others than solve(system; kwargs...) which renders them incompatible to the philosophy of `CommonSolve. Updated examples accordingly.
      • Deprecated the following entries of SolverControl/solve kwargs:   :tol_absolute => :abstol,   :tol_relative => :reltol,   :damp => :damp_initial,   :damp_grow => :damp_growth   :max_iterations => e:maxiters   :tol_linear => :reltol_linear   :max_lureuse =>
      • NewtonControl
      v0.18.8 - 0.18.10  Dec 11, 2022 - Jan 5, 2023
      • Internal restructuring: remove @create_physics_wrappers macro, reduce boilerplate in assembly, wrap repeating pattenrns into functions.  The price in the moment is a bit of a slowdown of assembly.
      • Fix parameter dependency handling (now we can get parameter derivative without solving in dual numbers; see the runh() example in Example430. However in the moment the advantatge is not very clear, so this  is on hold...
      v0.18.7  Dec 7, 2022
      • bump gridvisualize compat
      v0.18.6  Dec 3, 2022
      • enable non-diagonal mass matrices for VoronoiFVMDiffEq
      v0.18.5  Nov 30, 2022
      • ready for Julia 1.9, re-enable CI on nighly
      v0.18.4  Nov 29, 2022
      • Add API methods used by VoronoiFVMDiffEq.jl
      v0.18.3  Oct 18 2022
      • Removed some allocations
      v0.18.2  Oct 13 2022
      • Emerging capability of differencing wrt. parameters (experimental, see example 430)
      • Allow iterative methods from Krylov.jl
      • Proper Dirichlet initialization with bcondition
      • Allow for more general matrix structures (banded, tridiagonal, multidiagonal)
      v0.18.1 September 25 2022
      • Working spherical symmetry case
      v0.18 September 12 2022
      • Remove DifferentialEquations interface (move this to a glue package)
      The current method of activating it through require is too brittle with respect to versioning.
      v0.17.1 August 20 2022
      • Fix DifferentialEquations interface, start transition to LinearSolve
      v0.17.0 July 1 2022
      • ensure not to assemble data for species where they are not enabled  This change should be breaking only for incorrect code where physics callbacks write into degrees of freedom which are not enabled
      v0.16.5 June 30, 2022
      • add iteration to solver options, allow to choose :cg, :bicgstab.
      • allow setting penalty with boundary_dirichlet!
      v0.16.4 May 25, 2022
      • fix x-t plots 
      v0.16.3 March 18, 2022
      • Linearization API
      • relax some type constraints
      v0.16.2 Feb 18, 2022
      • ExtendableGrids 0.9
      v0.16.1 Feb 17, 2022
      • fix quantity postprocessing
      • define unknown access for abstract vectors instead of vectors
      • pass rhs/unknowns wrappers in postprocessing methods
      • integrals as a wrapper type with proper quantity handling
      v0.16.0 Feb 13, 2022
      • Expose ODEProblem (and possibly ODEFunc) from VoronoiFVM.System.
      • Breaking: Remove solve wrapper for DifferentialEquations.solve, instead recommend to call that directly
      • Breaking: Handle DifferentialEquations.jl via Requires.jl.
      v0.15.1 Jan 15, 2022
      • Documentation fixes
      • Fix OrdinaryDiffEq interface
      • added example for current calculation with Quantities
      • Fixed type instabilities in quantities interface 
      v0.15.0 Jan 1, 2022
      • Breaking: History is not anymore returned by solve, instead it can be accessed via history after the solution.
      • Cleaned API:
      • OrdinaryDiffEq solver now in CI
      • scalarplot for 1D transient solutions
      • Sparsity detection via Symbolics.jl instead of the sunsetted SparsityDetection.jl
      v0.14.0 Dec 24, 2021
      Backward compatible, hopefully nonbreaking API simplification
      • Boundary conditions are now specified in breaction. Advantages:
        • easy x/t dependency
        • unified (upcoming) interface for parameters
        • unified handling of standard and nonstandard boundary conditions
        • simpler documentation
      • Made NewtonControl alias of SolverControl, continue to work with SolverControl
      • System constructor now directly takes physics callback functions, no need anymore to work with extra physics struct
      • solve() now takes "SolverControl" parameters as kwargs,no need anymore to work with extra NewtonControl/SolverControl struct
      • Notebooks as part of documentation and CI
      • See also the pluto notebook api-update.jl
      v0.13.2 Oct 29, 2021
      • Bernoulli function overhaul
      v0.13.1
      • sorted things with ExtendableGrids
      • nodal flux reconstruction (e.g. for visualization)
      v0.13.0, Oct 13, 2021
      • various bug fixes, explicit numbering of edge nodes
      v0.12.3, July 7, 2021
      • Add quantity id
      • Document quantities
      v0.12.2, July 7, 2021
      Introduce the notion of quantities which can be continuous or discontinuous at interfaces.
      • Quantity handling is implemented on top of species handling
      • Unknowns u and rhs y now passed to callbacks as wrapper types,  and can be indexed by quantity or by species numbers.  Moreover, this will allow to abstract parameters, gradients etc. in future versions.
      v0.12.0, July 2 2021
      • By default, the u parameter in flux callbacks is now a  nspec x 2 array
      • unknowns(edge,u), viewK, viewL are obsolete, they still work for backward compatibility
      • physics.num_species is now meaningless, num_species is automatically detected.
      • SparseSystem and DenseSystem are now type aliases of a parametrized type instead of two  independent subtypes of System
      v0.11.8
      • increase chunk size threshold to match argument length in calls to vectormodejacobian
      v0.11.7
      • First attempts on surface flux
      v0.11.1, April 13, 2021
      • Assembly loops cleaned from type instabilities
      • Optionally check for allocations due to type instabilities introduced in physics callbacks. See check_allocs! for more information.
      v0.11, April 12, 2021
      • Depending on Julia 1.5 now
      • Lineaer solvers now based on factorize! from ExtendableSparse 0.5
      • Documentation overhaul
      • Re-checking impedance calculation
      v0.10.13 April 1, 2021
      • Outflow boundary conditions
      v0.10.8 March 22, 2021
      • TransientSolution structure, transient solve
      • Solve compatible with DifferentialEquations.jl
      v0.10.3 Feb 11, 2021
      • Introduce non-mutating solve
      • Optionally record history if log kw is true in solve.
      v0.10.0 Jan 9 2021
      • Moving visualization to the package GridVisualize.jl, emerging from  the visualization methods in ExtendableGrids
      v0.9.0 Dec 21 2020
      • Add the possibility to interface with DifferentialEquations.jl
      • Breaking: The API change to passing the unknowns to the an edge callback as a matrix turned out to be a dead end in the strategic sense. In order to extend functionality, we need to be able to pass more data to  which we can apply differetiation. Particular plans involve bifurcation parameters and reconstructed gradients. So we return to the viewK/viewL pattern we had before. However,  these are now aliases:
        • viewK(edge,u)=unknowns(edge,u,1)
        • viewL(edge,u)=unknowns(edge,u,2)
        In order to ease refactoring in the case where models have been implemented with Matrix access to the unknowns, unknowns(edge,u) returns a matrix of the edge unknowns.    For refactoring, just rewrite e.g.
          function flux(y,u,edge)
         for ispec=1:nspec
             y[ispec]=u[ispec,1]-u[ispec,2]
         end
@@ -8,4 +8,4 @@
         for ispec=1:nspec
             y[ispec]=u[ispec,1]-u[ispec,2]
         end
-    end
      v0.8.5 Sep 1 2020
      • allow any object in Physics.data  (thanks Jan Weidner)
      • add generic operator for non-canonical problem structures
      v0.8.4 July 25 2020
      • Update ExtendableGrids + ExtendableSparse
      v0.8.3 June 25 2020
      • Replace splatting by dispatch on availability of data record
      v0.8.2 May 15 2020
      • Form factors are now pre-calculated and stored
      • Introduced update_grid! for triggering re-calculation if coordinates have changed
      v0.8.1 May 2 2020
      • Introduce evolve! : time solver with automatic timestep control
      v0.8 Apr 28, 2020
      • Replaced VoronoiFVM grid module by  ExtendableGrids.jl
      • Moved grid generation, modification, plotting  over to ExtendableGrids
      • Necessary changes in codes using VoronoiFVM:
        • Replace grid.coord by coord obtained via coord=coordinates(grid) or  coord=grid[Coordinates] after importing ExtendableGrids
        • Replace VoronoiFVM.plot by ExtendableGrids.plot.
        • In the plot method, Plotter is now a keyword argument
        • VoronoiFVM.Grid() now returns a ExtendableGrids.ExtendableGrid,  in fact it is just an alias to ExtendableGrids.simplexgrid
        • For using any methods on grids like cellmask! one needs to use ExtendableGrids
        • Subgrids now are of the same type ExtendableGrids,  views are currently defined for vectors only.
      v0.7 Feb 28 2020
      • API modification:
        • Breaking:
          • data parameter passed to physics callbacks only if Physics object is created with data parameter.
            This makes the API more consistent in the case that parameters are just taken from the closure (the scope where the physics functions are defined) and no data object has been created.
          • Replace node.coord[i] by  node[i].
          • Replace edge.coordK[i] by  edge[i,1].
          • Replace edge.coordL[i] by  edge[i,2].
            This now directly accesses the coordinate field of the grid and avoids copying of the coordinates
        • Backward compatible:  
          • No need for viewK and viewL in edge callbacks (they also make trouble with allocations...)
            • Replace uk[i] by u[i,1]
            • Replace ul[i] by u[i,2]
          • Replace VoronoiFVM.DenseSystem(...)  by VoronoiFVM.System(..., unknown_storage=:dense)
          • Replace VoronoiFVM.SparseSystem(...) by VoronoiFVM.System(..., unknown_storage=:sparse)
      • No allocations anymore in assembly loop:
        • Replaced ElasticArray in Grid by normal one - this was the largest regression
        • Return nothing from mutating methods to avoid some allocations 
        • Indexing in formfactors.jl with Int
      v0.6.5 Jan 25 2020
      • use updateindex! for matrix, depend on ExtendableSparse 0.2.6
      v0.6.4 2020-01-20
      • Rearranged + commented boundary assembly loop
      • Reworked + renamed some examples
      • Document that unknowns doesn't initialize values.
      v0.6.3 2019-12-21
      remove xcolptrs call Update dependency on ExtendableSparse
      v0.6.2 2019-12-20
      Updated dependency list (Triangulate ^0.4.0)
      v0.6.1, 2019-12-17
      • return "plotted" for being able to  place colormap
      • require Triangulate >= 0.3.0
      v0.6.0, Dec 15 2019
      • Removed Triangle submodule, depend on new Triangulate.jl Triangle wrapper
      • link to source code in examples
      • boundary_dirichlet! etc methods for setting boundary conditions
      v0.5.6 Dec 5 2019
      • Bug fixes
      • check triangle input for min 3 points
      • check triangle edgelist for C_NULL
      • voronoi plot
      v0.5.5 Dec 4 2019
      • (Temporary) Copy of TriangleRaw as Triangle submodule. To be replaced by dependency on evisioned package
      v0.5.4 Dec 3 2019
      • Re-enabled ElasticArrays in grid structure (for the time being)
      • Added potkink example: this adds an inner boundary
      v0.5.3 Dec 1 2019
      • triangle in optional submodule
      • Modified API for plotting
        • Removed formal dependency on Plots and PyPlot
        • Use Plotter module as first parameter to plot methods  - replaces fvmplot and fvmpyplot functions. Use VoronoiFVM.plot(PyPlot,...) resp.  VoronoiFVM.plot(Plots,...)
        • No more complaints when package is used in environment with plots or pyplot installed
      • Modified API for impedance
      v0.5.2 Nov 19, 2019
      • Reorganized grid stuff
      • Included triangle (after Ideas from TriangleMesh.jl)
      v0.5.1 Nov 13, 2019
      • Fixed performance regression: AbstractArrays for Grid components were slow.
      • Added handling of cylindrical coordinates
      V0.5, November 10, 2019
      • Velocity projections
      • Added edge handling to grid struct
      V0.4.2, November 6, 2019
      • Replaced PyPlot by Plots
      • Better and more examples
      V0.4, July 12, 2019
      • Registered with Julia ecosystem
      • Enhance Newton solver by embedding, exception handling
      • Replace SparseMatrixCSC with ExtendableSparseMatrix
      • fixed allocation issues in assembly
      • assured that users get allocation stuff right via typed functions in physics structure
      • more julianic API
      V0.3, April 9 2019
      • Renamed from TwoPointFluxFVM to  VoronoiFVM
      • Complete rewrite of assembly allowing sparse or dense matrix  to store degree of freedom information
        • Solution is a nnodes x nspecies sparse or dense matrix
        • The wonderful array interface of Julia still provides slicing etc in order to access species without need to write any bulk_solution stuff or whatever when using the sparse variant
      • Re-export value() for debugging in physics functions
      • Test function handling for flux calculation
      • First working steps to impedance handling
      • Abolished Graph in favor of  Grid, Graph was premature optimization...
      V0.2, Feb 20, 2019
      • Changed signature of all callback functions: This also allows to pass user defined arrays etc. to the callback functions. In particular, velocity vectors can be passed this way.
        • Besides of flux!(), they now all have node::VoronoiFVM.Node as a second argument.
        • flux!() has edge::VoronoiFVM.Edge as a second argument
        • the x argument in source!() is omitted, the same data  are now found in node.coord
      • New method edgelength(edge::VoronoiFVM.Edge)
      V0.1, Dec. 2018
      • Initial release
      
+    end

      v0.8.5 Sep 1 2020

      • allow any object in Physics.data (thanks Jan Weidner)
      • add generic operator for non-canonical problem structures

      v0.8.4 July 25 2020

      • Update ExtendableGrids + ExtendableSparse

      v0.8.3 June 25 2020

      • Replace splatting by dispatch on availability of data record

      v0.8.2 May 15 2020

      • Form factors are now pre-calculated and stored
      • Introduced update_grid! for triggering re-calculation if coordinates have changed

      v0.8.1 May 2 2020

      • Introduce evolve! : time solver with automatic timestep control

      v0.8 Apr 28, 2020

      • Replaced VoronoiFVM grid module by ExtendableGrids.jl
      • Moved grid generation, modification, plotting over to ExtendableGrids
      • Necessary changes in codes using VoronoiFVM:
        • Replace grid.coord by coord obtained via coord=coordinates(grid) or coord=grid[Coordinates] after importing ExtendableGrids
        • Replace VoronoiFVM.plot by ExtendableGrids.plot.
        • In the plot method, Plotter is now a keyword argument
        • VoronoiFVM.Grid() now returns a ExtendableGrids.ExtendableGrid, in fact it is just an alias to ExtendableGrids.simplexgrid
        • For using any methods on grids like cellmask! one needs to use ExtendableGrids
        • Subgrids now are of the same type ExtendableGrids, views are currently defined for vectors only.

      v0.7 Feb 28 2020

      • API modification:

        • Breaking:

          • data parameter passed to physics callbacks only if Physics object is created with data parameter.

            This makes the API more consistent in the case that parameters are just taken from the closure (the scope where the physics functions are defined) and no data object has been created.

          • Replace node.coord[i] by node[i].

          • Replace edge.coordK[i] by edge[i,1].

          • Replace edge.coordL[i] by edge[i,2].

            This now directly accesses the coordinate field of the grid and avoids copying of the coordinates

        • Backward compatible:

          • No need for viewK and viewL in edge callbacks (they also make trouble with allocations...)
            • Replace uk[i] by u[i,1]
            • Replace ul[i] by u[i,2]
          • Replace VoronoiFVM.DenseSystem(...) by VoronoiFVM.System(..., unknown_storage=:dense)
          • Replace VoronoiFVM.SparseSystem(...) by VoronoiFVM.System(..., unknown_storage=:sparse)

      • No allocations anymore in assembly loop:

        • Replaced ElasticArray in Grid by normal one - this was the largest regression
        • Return nothing from mutating methods to avoid some allocations
        • Indexing in formfactors.jl with Int

      v0.6.5 Jan 25 2020

      • use updateindex! for matrix, depend on ExtendableSparse 0.2.6

      v0.6.4 2020-01-20

      • Rearranged + commented boundary assembly loop
      • Reworked + renamed some examples
      • Document that unknowns doesn't initialize values.

      v0.6.3 2019-12-21

      remove xcolptrs call Update dependency on ExtendableSparse

      v0.6.2 2019-12-20

      Updated dependency list (Triangulate ^0.4.0)

      v0.6.1, 2019-12-17

      • return "plotted" for being able to place colormap
      • require Triangulate >= 0.3.0

      v0.6.0, Dec 15 2019

      • Removed Triangle submodule, depend on new Triangulate.jl Triangle wrapper
      • link to source code in examples
      • boundary_dirichlet! etc methods for setting boundary conditions

      v0.5.6 Dec 5 2019

      • Bug fixes
      • check triangle input for min 3 points
      • check triangle edgelist for C_NULL
      • voronoi plot

      v0.5.5 Dec 4 2019

      • (Temporary) Copy of TriangleRaw as Triangle submodule. To be replaced by dependency on evisioned package

      v0.5.4 Dec 3 2019

      • Re-enabled ElasticArrays in grid structure (for the time being)
      • Added potkink example: this adds an inner boundary

      v0.5.3 Dec 1 2019

      • triangle in optional submodule
      • Modified API for plotting
        • Removed formal dependency on Plots and PyPlot
        • Use Plotter module as first parameter to plot methods - replaces fvmplot and fvmpyplot functions. Use VoronoiFVM.plot(PyPlot,...) resp. VoronoiFVM.plot(Plots,...)
        • No more complaints when package is used in environment with plots or pyplot installed
      • Modified API for impedance

      v0.5.2 Nov 19, 2019

      • Reorganized grid stuff
      • Included triangle (after Ideas from TriangleMesh.jl)

      v0.5.1 Nov 13, 2019

      • Fixed performance regression: AbstractArrays for Grid components were slow.
      • Added handling of cylindrical coordinates

      V0.5, November 10, 2019

      • Velocity projections
      • Added edge handling to grid struct

      V0.4.2, November 6, 2019

      • Replaced PyPlot by Plots
      • Better and more examples

      V0.4, July 12, 2019

      • Registered with Julia ecosystem
      • Enhance Newton solver by embedding, exception handling
      • Replace SparseMatrixCSC with ExtendableSparseMatrix
      • fixed allocation issues in assembly
      • assured that users get allocation stuff right via typed functions in physics structure
      • more julianic API

      V0.3, April 9 2019

      • Renamed from TwoPointFluxFVM to VoronoiFVM
      • Complete rewrite of assembly allowing sparse or dense matrix to store degree of freedom information
        • Solution is a nnodes x nspecies sparse or dense matrix
        • The wonderful array interface of Julia still provides slicing etc in order to access species without need to write any bulk_solution stuff or whatever when using the sparse variant
      • Re-export value() for debugging in physics functions
      • Test function handling for flux calculation
      • First working steps to impedance handling
      • Abolished Graph in favor of Grid, Graph was premature optimization...

      V0.2, Feb 20, 2019

      • Changed signature of all callback functions: This also allows to pass user defined arrays etc. to the callback functions. In particular, velocity vectors can be passed this way.

        • Besides of flux!(), they now all have node::VoronoiFVM.Node as a second argument.

        • flux!() has edge::VoronoiFVM.Edge as a second argument

        • the x argument in source!() is omitted, the same data are now found in node.coord

      • New method edgelength(edge::VoronoiFVM.Edge)

      V0.1, Dec. 2018

      • Initial release
      diff --git a/dev/devel/index.html b/dev/devel/index.html index ebcb53996..8585c5449 100644 --- a/dev/devel/index.html +++ b/dev/devel/index.html @@ -1,2 +1,2 @@ -Development hints · VoronoiFVM.jl
      Edit on GitHub

      Development hints

      Here, a bit of development hints are given which mainly concern tests and documentation generation.

      Pluto notebooks

      The pluto notebooks in this package are "triple use":

      • As typical Pluto notebooks, they are self-contained in the senses that they contain their own Project and Manifest files. So users can just download and execute them.
      • If they run with the environmnet variable PLUTO_PROJECT set to some julia environment, this environment will activated at the start of the notebook. In particular, they use Revise.jl so they can be run during development

      of VoronoiFVM.jl. See also https://github.com/fonsp/Pluto.jl/issues/1788 .

      • During CI tests, they are run as scripts. For this purpose they are wrapped into temporariy modules, and @test macros can used in the notebooks.
      +Development hints · VoronoiFVM.jl

      Development hints

      Here, a bit of development hints are given which mainly concern tests and documentation generation.

      Pluto notebooks

      The pluto notebooks in this package are "triple use":

      • As typical Pluto notebooks, they are self-contained in the senses that they contain their own Project and Manifest files. So users can just download and execute them.
      • If they run with the environmnet variable PLUTO_PROJECT set to some julia environment, this environment will activated at the start of the notebook. In particular, they use Revise.jl so they can be run during development

      of VoronoiFVM.jl. See also https://github.com/fonsp/Pluto.jl/issues/1788 .

      • During CI tests, they are run as scripts. For this purpose they are wrapped into temporariy modules, and @test macros can used in the notebooks.
      diff --git a/dev/examples/Example001_Solvers/index.html b/dev/examples/Example001_Solvers/index.html index e5055e4d5..286ee7f46 100644 --- a/dev/examples/Example001_Solvers/index.html +++ b/dev/examples/Example001_Solvers/index.html @@ -1,5 +1,5 @@ -001: New linear solver API · VoronoiFVM.jl
      Edit on GitHub

      001: New linear solver API

      (source code)

      module Example001_Solvers

      under development

      using Printf
+001: New linear solver API · VoronoiFVM.jl
      001: New linear solver API
      (source code)
      module Example001_Solvers
      under development
      using Printf
 using VoronoiFVM
 using ExtendableGrids
 using GridVisualize
@@ -112,4 +112,4 @@
 function test()
     main(assembly=:edgewise) &&  main(assembly=:cellwise)
 end
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example002_EdgeReaction/index.html b/dev/examples/Example002_EdgeReaction/index.html index 79f1d4cad..a8bcca061 100644 --- a/dev/examples/Example002_EdgeReaction/index.html +++ b/dev/examples/Example002_EdgeReaction/index.html @@ -1,5 +1,5 @@ -002: check edge reaction · VoronoiFVM.jl
      Edit on GitHub

      002: check edge reaction

      (source code)

      module Example002_EdgeReaction
+002: check edge reaction · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example101_Laplace1D/index.html b/dev/examples/Example101_Laplace1D/index.html index 04df176a5..d66d12000 100644 --- a/dev/examples/Example101_Laplace1D/index.html +++ b/dev/examples/Example101_Laplace1D/index.html @@ -1,5 +1,5 @@ -101: 1D Laplace equation · VoronoiFVM.jl
      Edit on GitHub

      101: 1D Laplace equation

      (source code)

      Let $\Omega=(\gamma_1,\gamma_2)$ with $\gamma_1=0$, $\gamma_2=1$. This is the simplest second order boundary value problem (BVP) for a partial differential equation (PDE):

      \[-\Delta u =0\\ +101: 1D Laplace equation · VoronoiFVM.jl

      101: 1D Laplace equation

      (source code)

      Let $\Omega=(\gamma_1,\gamma_2)$ with $\gamma_1=0$, $\gamma_2=1$. This is the simplest second order boundary value problem (BVP) for a partial differential equation (PDE):

      \[-\Delta u =0\\ u(\gamma_1)=g_1\\ u(\gamma_2)=g_2.\]

      We replace the Dirichlet boundary condition by a Robin boundary condition with a penalty parameter $\frac{1}{\varepsilon}$:

      \[\nabla u(\gamma_1) + \frac{1}{\varepsilon}(u(\gamma_1)-g_1)=0 \\ -\nabla u(\gamma_2) + \frac{1}{\varepsilon}(u(\gamma_2)-g_2) @@ -57,4 +57,4 @@ main() ≈ 3.0 end -end

      This page was generated using Literate.jl.

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example102_StationaryConvectionDiffusion1D/index.html b/dev/examples/Example102_StationaryConvectionDiffusion1D/index.html index 40fa9fbbd..9db3b52a5 100644 --- a/dev/examples/Example102_StationaryConvectionDiffusion1D/index.html +++ b/dev/examples/Example102_StationaryConvectionDiffusion1D/index.html @@ -1,5 +1,5 @@ -102: 1D Stationary convection-diffusion equation · VoronoiFVM.jl
      Edit on GitHub

      102: 1D Stationary convection-diffusion equation

      (source code)

      Solve the equation

      \[-\nabla ( D \nabla u - v u) = 0\]

      in $\Omega=(0,1)$ with boundary condition $u(0)=0$ and $u(1)=1$. $v$ could be e.g. the velocity of a moving medium or the gradient of an electric field.

      This is a convection dominant second order boundary value problem which obeys a local and a global maximum principle: the solution which is bounded by the values at the boundary and has no local extrema in the interior. If $v$ is large compared to $D$, a boundary layer is observed.

      The maximum principle of the solution can only be guaranteed it the discretization is performed accordingly: the flux function must monotonically increase in the first argument and monotonically decrease in the second argument.

      The example describes three possible ways to define the flux function and demonstrates the impact on the qualitative properties of the solution.

      module Example102_StationaryConvectionDiffusion1D
+102: 1D Stationary convection-diffusion equation · VoronoiFVM.jl
      102: 1D Stationary convection-diffusion equation
      (source code)
      Solve the equation
      \[-\nabla ( D \nabla u - v u) = 0\]
      in $\Omega=(0,1)$ with boundary condition $u(0)=0$ and $u(1)=1$. $v$ could be e.g. the velocity of a moving medium or the gradient of an electric field.
      This is a convection dominant second order boundary value problem which obeys a local and a global maximum principle: the solution which is bounded by the values at the boundary and has no local extrema in the interior. If $v$ is large compared to $D$, a boundary layer is observed.
      The maximum principle of the solution can only be guaranteed it the discretization is performed accordingly: the flux function must monotonically increase in the first argument and monotonically decrease in the second argument.
      The example describes three possible ways to define the flux function and demonstrates the impact on the qualitative properties of the solution.
      module Example102_StationaryConvectionDiffusion1D
 using Printf
 using VoronoiFVM
 using ExtendableGrids
@@ -95,4 +95,4 @@
     main() ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example103_ConvectionDiffusion1D/index.html b/dev/examples/Example103_ConvectionDiffusion1D/index.html index 76abaab72..a464c0aed 100644 --- a/dev/examples/Example103_ConvectionDiffusion1D/index.html +++ b/dev/examples/Example103_ConvectionDiffusion1D/index.html @@ -1,5 +1,5 @@ -103: 1D Convection-diffusion equation · VoronoiFVM.jl
      Edit on GitHub

      103: 1D Convection-diffusion equation

      (source code)

      Solve the equation

      \[\partial_t u -\nabla ( D \nabla u - v u) = 0\]

      in $\Omega=(0,1)$ with homogeneous Neumann boundary condition at $x=0$ and outflow boundary condition at $x=1$.

      module Example103_ConvectionDiffusion1D
+103: 1D Convection-diffusion equation · VoronoiFVM.jl
      103: 1D Convection-diffusion equation
      (source code)
      Solve the equation
      \[\partial_t u -\nabla ( D \nabla u - v u) = 0\]
      in $\Omega=(0,1)$ with homogeneous Neumann boundary condition at $x=0$ and outflow boundary condition at $x=1$.
      module Example103_ConvectionDiffusion1D
 using Printf
 using VoronoiFVM
 using ExtendableGrids
@@ -69,4 +69,4 @@
     maximum(tsol) <= 1.0 && maximum(tsol[end]) < 1.0e-20
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example105_NonlinearPoisson1D/index.html b/dev/examples/Example105_NonlinearPoisson1D/index.html index 0de51dbba..0a3ac581e 100644 --- a/dev/examples/Example105_NonlinearPoisson1D/index.html +++ b/dev/examples/Example105_NonlinearPoisson1D/index.html @@ -1,5 +1,5 @@ -105: 1D Nonlinear Poisson equation · VoronoiFVM.jl
      Edit on GitHub

      105: 1D Nonlinear Poisson equation

      (source code)

      Solve the nonlinear Poisson equation

      \[-\nabla \varepsilon \nabla u + e^{u}-e^{-u} = f\]

      in $\Omega=(0,1)$ with boundary condition $u(0)=0$ and $u(1)=1$ with

      \[f(x)= +105: 1D Nonlinear Poisson equation · VoronoiFVM.jl

      105: 1D Nonlinear Poisson equation

      (source code)

      Solve the nonlinear Poisson equation

      \[-\nabla \varepsilon \nabla u + e^{u}-e^{-u} = f\]

      in $\Omega=(0,1)$ with boundary condition $u(0)=0$ and $u(1)=1$ with

      \[f(x)= \begin{cases} 1&,x>0.5\\ -1&, x<0.5 @@ -76,4 +76,4 @@ main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval end -end

      This page was generated using Literate.jl.

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example106_NonlinearDiffusion1D/index.html b/dev/examples/Example106_NonlinearDiffusion1D/index.html index 82f1f911b..a6a26c0fe 100644 --- a/dev/examples/Example106_NonlinearDiffusion1D/index.html +++ b/dev/examples/Example106_NonlinearDiffusion1D/index.html @@ -1,5 +1,5 @@ -106: 1D Nonlinear Diffusion equation · VoronoiFVM.jl
      Edit on GitHub

      106: 1D Nonlinear Diffusion equation

      (source code)

      Solve the nonlinear diffusion equation

      \[\partial_t u -\Delta u^m = 0\]

      in $\Omega=(-1,1)$ with homogeneous Neumann boundary conditions using the implicit Euler method.

      This equation is also called "porous medium equation". The Barenblatt solution is an exact solution of this problem which for m>1 has a finite support. We initialize this problem with the exact solution for $t=t_0=0.001$.

      (see Barenblatt, G. I. "On nonsteady motions of gas and fluid in porous medium." Appl. Math. and Mech.(PMM) 16.1 (1952): 67-78.)

      module Example106_NonlinearDiffusion1D
+106: 1D Nonlinear Diffusion equation · VoronoiFVM.jl
      106: 1D Nonlinear Diffusion equation
      (source code)
      Solve the nonlinear diffusion equation
      \[\partial_t u -\Delta u^m = 0\]
      in $\Omega=(-1,1)$ with homogeneous Neumann boundary conditions using the implicit Euler method.
      This equation is also called  "porous medium equation". The Barenblatt solution is an exact solution of this problem which for m>1 has a finite support. We initialize this problem with the exact solution for $t=t_0=0.001$.
      (see Barenblatt, G. I. "On nonsteady motions of gas and fluid in porous medium." Appl. Math. and Mech.(PMM) 16.1 (1952): 67-78.)
      module Example106_NonlinearDiffusion1D
 using Printf
 using VoronoiFVM
 using ExtendableGrids
@@ -88,4 +88,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example107_NonlinearStorage1D/index.html b/dev/examples/Example107_NonlinearStorage1D/index.html index 1fa84f1a6..db26cd85b 100644 --- a/dev/examples/Example107_NonlinearStorage1D/index.html +++ b/dev/examples/Example107_NonlinearStorage1D/index.html @@ -1,5 +1,5 @@ -107: 1D Nonlinear Storage · VoronoiFVM.jl
      Edit on GitHub

      107: 1D Nonlinear Storage

      (source code)

      This equation comes from the transformation of the nonlinear diffuision equation.

      \[\partial_t u^\frac{1}{m} -\Delta u = 0\]

      in $\Omega=(-1,1)$ with homogeneous Neumann boundary conditions. We can derive an exact solution from the Barenblatt solution of the previous example.

      module Example107_NonlinearStorage1D
+107: 1D Nonlinear Storage · VoronoiFVM.jl
      107: 1D Nonlinear Storage
      (source code)
      This equation comes from the transformation of the nonlinear diffuision equation.
      \[\partial_t u^\frac{1}{m} -\Delta u = 0\]
      in $\Omega=(-1,1)$ with homogeneous Neumann boundary conditions. We can derive an exact solution from the Barenblatt solution of the previous example.
      module Example107_NonlinearStorage1D
 using Printf
 using VoronoiFVM
 using ExtendableGrids
@@ -89,4 +89,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example110_ReactionDiffusion1D_TwoSpecies/index.html b/dev/examples/Example110_ReactionDiffusion1D_TwoSpecies/index.html index af7452b33..9adac5310 100644 --- a/dev/examples/Example110_ReactionDiffusion1D_TwoSpecies/index.html +++ b/dev/examples/Example110_ReactionDiffusion1D_TwoSpecies/index.html @@ -1,5 +1,5 @@ -110: 1D Reaction Diffusion equation with two species · VoronoiFVM.jl
      Edit on GitHub

      110: 1D Reaction Diffusion equation with two species

      (source code)

      Solve the nonlinear coupled reaction diffusion problem

      \[-\nabla (0.01+2u_2)\nabla u_1 + u_1u_2= 0.0001(0.01+x)\]

      \[-\nabla (0.01+2u_1)\nabla u_2 - u_1u_2 = 0.0001(1.01-x)\]

      in $\Omega=(0,1)$ with boundary condition $u_1(0)=1$, $u_2(0)=0$ and $u_1(1)=1$, $u_2(1)=1$.

      module Example110_ReactionDiffusion1D_TwoSpecies
+110: 1D Reaction Diffusion equation with two species · VoronoiFVM.jl
      110: 1D Reaction Diffusion equation with two species
      (source code)
      Solve the nonlinear coupled reaction diffusion problem
      \[-\nabla (0.01+2u_2)\nabla u_1 + u_1u_2= 0.0001(0.01+x)\]
      \[-\nabla (0.01+2u_1)\nabla u_2 - u_1u_2 = 0.0001(1.01-x)\]
      in $\Omega=(0,1)$ with boundary condition $u_1(0)=1$, $u_2(0)=0$ and $u_1(1)=1$, $u_2(1)=1$.
      module Example110_ReactionDiffusion1D_TwoSpecies
 
 using Printf
 using VoronoiFVM
@@ -70,4 +70,4 @@
         main(; unknown_storage = :sparse, assembly=:cellwise) ≈ testval &&
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example115_HeterogeneousCatalysis1D/index.html b/dev/examples/Example115_HeterogeneousCatalysis1D/index.html index 57bf2d9b3..7f9618e1d 100644 --- a/dev/examples/Example115_HeterogeneousCatalysis1D/index.html +++ b/dev/examples/Example115_HeterogeneousCatalysis1D/index.html @@ -1,5 +1,5 @@ -115: 1D heterogeneous catalysis · VoronoiFVM.jl
      Edit on GitHub

      115: 1D heterogeneous catalysis

      (source code)

      Let $\Omega=(0,1)$, $\Gamma_1=\{0\}$, $\Gamma_2=\{1\}$ Regard a system of three species: $A,B,C$ and let $u_A=[A]$, $u_B=[B]$ and $u_C=[C]$ be their corresponding concentrations.

      Species $A$ and $B$ exist in the interior of the domain, species $C$ lives a the boundary $\Gamma_1$. We assume a heterogeneous reaction scheme where $A$ reacts to $C$ and $C$ reacts to $B$:

      \[\begin{aligned} +115: 1D heterogeneous catalysis · VoronoiFVM.jl

      115: 1D heterogeneous catalysis

      (source code)

      Let $\Omega=(0,1)$, $\Gamma_1=\{0\}$, $\Gamma_2=\{1\}$ Regard a system of three species: $A,B,C$ and let $u_A=[A]$, $u_B=[B]$ and $u_C=[C]$ be their corresponding concentrations.

      Species $A$ and $B$ exist in the interior of the domain, species $C$ lives a the boundary $\Gamma_1$. We assume a heterogeneous reaction scheme where $A$ reacts to $C$ and $C$ reacts to $B$:

      \[\begin{aligned} A &\leftrightarrow C\\ C &\leftrightarrow B \end{aligned}\]

      with reaction constants $k_{AC}^\pm$ and k_{BC}^\pm$.

      In $\Omega$, both $A$ and $B$ are transported through diffusion:

      \[\begin{aligned} @@ -140,4 +140,4 @@ isapprox(main(; unknown_storage = :sparse, assembly=:cellwise), testval; rtol = 1.0e-12) && isapprox(main(; unknown_storage = :dense, assembly=:cellwise), testval; rtol = 1.0e-12) end -end

      This page was generated using Literate.jl.

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example120_ThreeRegions1D/index.html b/dev/examples/Example120_ThreeRegions1D/index.html index c86bc6e83..5c0fcac0d 100644 --- a/dev/examples/Example120_ThreeRegions1D/index.html +++ b/dev/examples/Example120_ThreeRegions1D/index.html @@ -1,5 +1,5 @@ -120: Differing species sets in regions, 1D · VoronoiFVM.jl
      Edit on GitHub

      120: Differing species sets in regions, 1D

      (source code)

      module Example120_ThreeRegions1D
+120: Differing species sets in regions, 1D · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example121_PoissonPointCharge1D/index.html b/dev/examples/Example121_PoissonPointCharge1D/index.html index 393e50c13..10baefde1 100644 --- a/dev/examples/Example121_PoissonPointCharge1D/index.html +++ b/dev/examples/Example121_PoissonPointCharge1D/index.html @@ -1,5 +1,5 @@ -121: 1D Poisson with point charge · VoronoiFVM.jl
      Edit on GitHub

      121: 1D Poisson with point charge

      (source code)

      Solve a Poisson equation

      \[- \Delta u = 0\]

      in $\Omega=(-1,1)$ with a point charge $Q$ at $x=0$.

      module Example121_PoissonPointCharge1D
+121: 1D Poisson with point charge · VoronoiFVM.jl
      121: 1D Poisson with point charge
      (source code)
      Solve a Poisson equation
      \[- \Delta u = 0\]
      in $\Omega=(-1,1)$ with a point charge $Q$ at $x=0$.
      module Example121_PoissonPointCharge1D
 
 using Printf
 
@@ -92,4 +92,4 @@
     main(assembly=:edgewise) ≈ testval &&
     main(assembly=:cellwise) ≈ testval
 end
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example125_TestFunctions1D/index.html b/dev/examples/Example125_TestFunctions1D/index.html index 1e78bafe6..54e63d9dc 100644 --- a/dev/examples/Example125_TestFunctions1D/index.html +++ b/dev/examples/Example125_TestFunctions1D/index.html @@ -1,5 +1,5 @@ -125: Terminal flux calculation via test functions · VoronoiFVM.jl
      Edit on GitHub

      125: Terminal flux calculation via test functions

      (source code)

      For a rather comprehensive explanation see 225: Terminal flux calculation via test functions, nD

      module Example125_TestFunctions1D
+125: Terminal flux calculation via test functions · VoronoiFVM.jl
      125: Terminal flux calculation via test functions
      (source code)
      For a rather comprehensive explanation see 225: Terminal flux calculation via test functions, nD
      module Example125_TestFunctions1D
 using Printf
 using VoronoiFVM
 using ExtendableGrids
@@ -64,4 +64,4 @@
         main(; unknown_storage = :sparse, assembly=:cellwise) ≈ testval &&
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example150_Impedance1D/index.html b/dev/examples/Example150_Impedance1D/index.html index 3ab3ba0c7..5af9ed839 100644 --- a/dev/examples/Example150_Impedance1D/index.html +++ b/dev/examples/Example150_Impedance1D/index.html @@ -1,5 +1,5 @@ -150: Impedance calculation · VoronoiFVM.jl
      Edit on GitHub

      150: Impedance calculation

      (source code)

      Impedance calculation for

      C ut - (D ux)_x + Ru = 0 in (0,1) u(0,t)=1 + exp(iωt) u(1,t)=0

      Measurement: I(t)= D u_x(1,t)

      Steady state:

      • (D u0x)x + Ru0 = 0

      u0(0,t)=1 u0(1,t)=0

      Small signal ansatz for ω

      u(x,t)= u0(x)+ ua(x) exp(iωt)

      iωC ua - (D uax)x + R u_a =0 ua(0)=1 ua(1)=0

      module Example150_Impedance1D
+150: Impedance calculation · VoronoiFVM.jl
      150: Impedance calculation
      (source code)
      Impedance calculation for
      C ut - (D ux)_x + Ru = 0   in (0,1)      u(0,t)=1 + exp(iωt)      u(1,t)=0
      Measurement: I(t)= D u_x(1,t)
      Steady state:
      • (D u0x)x + Ru0 = 0
      u0(0,t)=1    u0(1,t)=0
      Small signal ansatz for ω
      u(x,t)= u0(x)+ ua(x) exp(iωt)
      iωC ua - (D uax)x + R u_a =0      ua(0)=1      ua(1)=0
      module Example150_Impedance1D
 
 using Printf
 using VoronoiFVM
@@ -86,4 +86,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example151_Impedance1D/index.html b/dev/examples/Example151_Impedance1D/index.html index 79bf457df..6827b27bf 100644 --- a/dev/examples/Example151_Impedance1D/index.html +++ b/dev/examples/Example151_Impedance1D/index.html @@ -1,5 +1,5 @@ -151: Impedance calculation · VoronoiFVM.jl
      Edit on GitHub

      151: Impedance calculation

      (source code)

      Same as Example150, but with new and more generic way of passing the parameter.

      Impedance calculation for

      C ut - (D ux)_x + Ru = 0 in (0,1) u(0,t)=1 + exp(iωt) u(1,t)=0

      Measurement: I(t)= D u_x(1,t)

      Steady state:

      • (D u0x)x + Ru0 = 0

      u0(0,t)=1 u0(1,t)=0

      Small signal ansatz for ω

      u(x,t)= u0(x)+ ua(x) exp(iωt)

      iωC ua - (D uax)x + R u_a =0 ua(0)=1 ua(1)=0

      module Example151_Impedance1D
+151: Impedance calculation · VoronoiFVM.jl
      151: Impedance calculation
      (source code)
      Same as Example150, but with new and more generic way of  passing the parameter.
      Impedance calculation for
      C ut - (D ux)_x + Ru = 0   in (0,1)      u(0,t)=1 + exp(iωt)      u(1,t)=0
      Measurement: I(t)= D u_x(1,t)
      Steady state:
      • (D u0x)x + Ru0 = 0
      u0(0,t)=1    u0(1,t)=0
      Small signal ansatz for ω
      u(x,t)= u0(x)+ ua(x) exp(iωt)
      iωC ua - (D uax)x + R u_a =0      ua(0)=1      ua(1)=0
      module Example151_Impedance1D
 
 using Printf
 using VoronoiFVM
@@ -91,4 +91,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example160_UnipolarDriftDiffusion1D/index.html b/dev/examples/Example160_UnipolarDriftDiffusion1D/index.html index b0ff01d19..8d831c2cd 100644 --- a/dev/examples/Example160_UnipolarDriftDiffusion1D/index.html +++ b/dev/examples/Example160_UnipolarDriftDiffusion1D/index.html @@ -1,5 +1,5 @@ -160: Unipolar degenerate drift-diffusion · VoronoiFVM.jl
      Edit on GitHub

      160: Unipolar degenerate drift-diffusion

      (source code)

      See: C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, and B. Gaudeul, "A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model" IMA Journal of Numerical Analysis, vol. 41, no. 1, pp. 271–314, 2021.

      Available from https://doi.org/10.1093/imanum/draa002, the preprint is on arxiv1907.11126.

      The problem consists of a Poisson equation for the electrostatic potential $\phi$:

      \[-\nabla \varepsilon \nabla \phi = z(2c-1)\]

      and a degenerate drift-diffusion equation of the transport of a charged species $c$:

      \[\partial_t u - \nabla\cdot \left(\nabla c + c \nabla (\phi - \log (1-c) )\right)\]

      In particular, the paper, among others, investigates the "sedan" flux discretization which is able to handle the degeneracy coming from the $\log (1-c)$ term. The earliest reference to this scheme we found in the source code of the SEDAN III semiconductor device simulator.

      module Example160_UnipolarDriftDiffusion1D
+160: Unipolar degenerate drift-diffusion · VoronoiFVM.jl
      160: Unipolar degenerate drift-diffusion
      (source code)
      See: C. Cancès, C. Chainais-Hillairet, J. Fuhrmann, and B. Gaudeul, "A numerical-analysis-focused comparison of several finite volume schemes for a unipolar degenerate drift-diffusion model" IMA Journal of Numerical Analysis, vol. 41, no. 1, pp. 271–314, 2021.
      Available from https://doi.org/10.1093/imanum/draa002, the preprint is on arxiv1907.11126.
      The problem consists of a Poisson equation for the electrostatic potential $\phi$:
      \[-\nabla \varepsilon \nabla \phi = z(2c-1)\]
      and a degenerate drift-diffusion equation of the transport of a charged species $c$:
      \[\partial_t u  - \nabla\cdot \left(\nabla c  + c \nabla (\phi - \log (1-c) )\right)\]
      In particular, the paper, among others, investigates the "sedan" flux discretization which is able to handle the degeneracy coming from the $\log (1-c)$ term. The earliest reference to this scheme we found in the source code of the SEDAN III semiconductor device simulator.
      module Example160_UnipolarDriftDiffusion1D
 
 using Printf
 
@@ -269,4 +269,4 @@
             )
     end
 end
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example201_Laplace2D/index.html b/dev/examples/Example201_Laplace2D/index.html index d710f51ec..0059c8b89 100644 --- a/dev/examples/Example201_Laplace2D/index.html +++ b/dev/examples/Example201_Laplace2D/index.html @@ -1,5 +1,5 @@ -201: 2D Laplace equation · VoronoiFVM.jl
      Edit on GitHub

      201: 2D Laplace equation

      (source code)

      module Example201_Laplace2D
+201: 2D Laplace equation · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example203_CoordinateSystems/index.html b/dev/examples/Example203_CoordinateSystems/index.html index 406548d14..54d2e5ffc 100644 --- a/dev/examples/Example203_CoordinateSystems/index.html +++ b/dev/examples/Example203_CoordinateSystems/index.html @@ -1,5 +1,5 @@ -203: Various coordinate systems · VoronoiFVM.jl
      Edit on GitHub

      203: Various coordinate systems

      (source code)

      module Example203_CoordinateSystems
+203: Various coordinate systems · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example204_HagenPoiseuille/index.html b/dev/examples/Example204_HagenPoiseuille/index.html index 54272a06c..55995f107 100644 --- a/dev/examples/Example204_HagenPoiseuille/index.html +++ b/dev/examples/Example204_HagenPoiseuille/index.html @@ -1,5 +1,5 @@ -204: 2D Convection in Hagen-Poiseuille flow · VoronoiFVM.jl
      Edit on GitHub

      204: 2D Convection in Hagen-Poiseuille flow

      (source code)

      Solve the equation

      \[\partial_t u -\nabla ( D \nabla u - v u) = 0\]

      in $\Omega=(0,L)\times (0,H)$ with dirichlet boundary conditions at $x=0$ and outflow boundary condition at $x=L$.

      module Example204_HagenPoiseuille
+204: 2D Convection in Hagen-Poiseuille flow · VoronoiFVM.jl
      204: 2D Convection in Hagen-Poiseuille flow
      (source code)
      Solve the equation
      \[\partial_t u -\nabla ( D \nabla u - v u) = 0\]
      in $\Omega=(0,L)\times (0,H)$ with dirichlet boundary conditions at $x=0$ and outflow boundary condition at $x=L$.
      module Example204_HagenPoiseuille
 using Printf
 using VoronoiFVM
 using ExtendableGrids
@@ -62,4 +62,4 @@
     all(tsol1[end] .≈ 1)
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example205_StagnationPoint/index.html b/dev/examples/Example205_StagnationPoint/index.html index 19faaf8bd..2d1c09f74 100644 --- a/dev/examples/Example205_StagnationPoint/index.html +++ b/dev/examples/Example205_StagnationPoint/index.html @@ -1,5 +1,5 @@ -205: Convection in axisymmetric stagnation point flow · VoronoiFVM.jl
      Edit on GitHub

      205: Convection in axisymmetric stagnation point flow

      (source code)

      Solve the equation

      \[\begin{aligned} +205: Convection in axisymmetric stagnation point flow · VoronoiFVM.jl

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example206_JouleHeat/index.html b/dev/examples/Example206_JouleHeat/index.html index a249175ff..d81d0246c 100644 --- a/dev/examples/Example206_JouleHeat/index.html +++ b/dev/examples/Example206_JouleHeat/index.html @@ -1,5 +1,5 @@ -206: 2D Joule heating · VoronoiFVM.jl
      Edit on GitHub

      206: 2D Joule heating

      (source code)

      \[\begin{aligned} +206: 2D Joule heating · VoronoiFVM.jl

      206: 2D Joule heating

      (source code)

      \[\begin{aligned} -\nabla \left\cdot (\kappa(T) \nabla \phi\right) &= 0\\ \partial_t (cT) - \nabla\cdot \left(\lambda \nabla T\right) &= \kappa(T) |\nabla \phi|^2\\ \kappa(T)&= \kappa_0 exp(\alpha(T-T0)) @@ -93,4 +93,4 @@ main(assembly=:edgewise) ≈ testval && main(assembly=:cellwise) ≈ testval end -end

      This page was generated using Literate.jl.

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example207_NonlinearPoisson2D/index.html b/dev/examples/Example207_NonlinearPoisson2D/index.html index e202696ae..4e378a76c 100644 --- a/dev/examples/Example207_NonlinearPoisson2D/index.html +++ b/dev/examples/Example207_NonlinearPoisson2D/index.html @@ -1,5 +1,5 @@ -207: 2D Nonlinear Poisson equation · VoronoiFVM.jl
      Edit on GitHub

      207: 2D Nonlinear Poisson equation

      (source code)

      module Example207_NonlinearPoisson2D
+207: 2D Nonlinear Poisson equation · VoronoiFVM.jl
      207: 2D Nonlinear Poisson equation
      (source code)
      module Example207_NonlinearPoisson2D
 
 using Printf
 using VoronoiFVM
@@ -71,4 +71,4 @@
         main(; unknown_storage = :sparse, method_linear = KrylovJL_CG(), precon_linear = ILUZeroPreconditioner, assembly=:cellwise) ≈testval &&
         main(; unknown_storage = :dense,  method_linear = KrylovJL_CG(), precon_linear = ILUZeroPreconditioner, assembly=:cellwise) ≈ testval
 end
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example210_NonlinearPoisson2D_Reaction/index.html b/dev/examples/Example210_NonlinearPoisson2D_Reaction/index.html index ef39ba63b..a893d0667 100644 --- a/dev/examples/Example210_NonlinearPoisson2D_Reaction/index.html +++ b/dev/examples/Example210_NonlinearPoisson2D_Reaction/index.html @@ -1,5 +1,5 @@ -210: 2D Nonlinear Poisson with reaction · VoronoiFVM.jl
      Edit on GitHub

      210: 2D Nonlinear Poisson with reaction

      (source code)

      module Example210_NonlinearPoisson2D_Reaction
+210: 2D Nonlinear Poisson with reaction · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example215_NonlinearPoisson2D_BoundaryReaction/index.html b/dev/examples/Example215_NonlinearPoisson2D_BoundaryReaction/index.html index f550aa45b..5c88692e7 100644 --- a/dev/examples/Example215_NonlinearPoisson2D_BoundaryReaction/index.html +++ b/dev/examples/Example215_NonlinearPoisson2D_BoundaryReaction/index.html @@ -1,5 +1,5 @@ -215: 2D Nonlinear Poisson with boundary reaction · VoronoiFVM.jl
      Edit on GitHub

      215: 2D Nonlinear Poisson with boundary reaction

      (source code)

      module Example215_NonlinearPoisson2D_BoundaryReaction
+215: 2D Nonlinear Poisson with boundary reaction · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example220_NonlinearPoisson2D_BoundarySpecies/index.html b/dev/examples/Example220_NonlinearPoisson2D_BoundarySpecies/index.html index 174b8d97f..ce992b94b 100644 --- a/dev/examples/Example220_NonlinearPoisson2D_BoundarySpecies/index.html +++ b/dev/examples/Example220_NonlinearPoisson2D_BoundarySpecies/index.html @@ -1,5 +1,5 @@ -220: 2D Nonlinear Poisson with boundary reaction and boundary species · VoronoiFVM.jl
      Edit on GitHub

      220: 2D Nonlinear Poisson with boundary reaction and boundary species

      (source code)

      module Example220_NonlinearPoisson2D_BoundarySpecies
+220: 2D Nonlinear Poisson with boundary reaction and boundary species · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example225_TestFunctions2D/index.html b/dev/examples/Example225_TestFunctions2D/index.html index 1463da633..1156953e2 100644 --- a/dev/examples/Example225_TestFunctions2D/index.html +++ b/dev/examples/Example225_TestFunctions2D/index.html @@ -1,5 +1,5 @@ -225: Terminal flux calculation via test functions, nD · VoronoiFVM.jl
      Edit on GitHub

      225: Terminal flux calculation via test functions, nD

      (source code)

      After calculating solutions based on the finite volume method, it may be interesting to obtain information about the solution besides of the graphical representation.

      Here, we focus on the following data:

      • integrals of the solution
      • flux through parts of the boundary

      Let us define the following reaction - diffusion system in a domain $\Omega$:

      \[\begin{aligned} +225: Terminal flux calculation via test functions, nD · VoronoiFVM.jl

      225: Terminal flux calculation via test functions, nD

      (source code)

      After calculating solutions based on the finite volume method, it may be interesting to obtain information about the solution besides of the graphical representation.

      Here, we focus on the following data:

      • integrals of the solution
      • flux through parts of the boundary

      Let us define the following reaction - diffusion system in a domain $\Omega$:

      \[\begin{aligned} \partial_t u_1 - \nabla \cdot \nabla u_1 + r(u_1, u_2) &= f=1.0\\ \partial_t u_2 - \nabla \cdot \nabla u_1 - r(u_1, u_2) &= 0 \end{aligned}\]

      with boundary conditions $u_2=0$ on $\Gamma_2\subset\partial\Omega$ and $r(u_1,u_2)=u_1 + 0.1 u_2$

      The source $f$ creates species $u_1$ which reacts to $u_2$, $u_2$ then leaves the domain at boundary $\Gamma_2$.

      Stationary problem

      For the stationary problem, we have the following flux balances derived from the equations and from Gauss theorem:

      \[\begin{aligned} @@ -163,4 +163,4 @@ main(; dim = 3, unknown_storage = :dense, assembly=:cellwise) ? true : return false end -end

      This page was generated using Literate.jl.

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example226_BoundaryIntegral/index.html b/dev/examples/Example226_BoundaryIntegral/index.html index 8140c1869..80b215717 100644 --- a/dev/examples/Example226_BoundaryIntegral/index.html +++ b/dev/examples/Example226_BoundaryIntegral/index.html @@ -1,5 +1,5 @@ -226: Terminal flux calculation via test functions, nD, boundary reaction · VoronoiFVM.jl
      Edit on GitHub

      226: Terminal flux calculation via test functions, nD, boundary reaction

      (source code)

      module Example226_BoundaryIntegral
+226: Terminal flux calculation via test functions, nD, boundary reaction · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example230_BoundaryFlux/index.html b/dev/examples/Example230_BoundaryFlux/index.html index f22bf250f..a8cb1abc5 100644 --- a/dev/examples/Example230_BoundaryFlux/index.html +++ b/dev/examples/Example230_BoundaryFlux/index.html @@ -1,5 +1,5 @@ -103: Boundary flux · VoronoiFVM.jl
      Edit on GitHub

      103: Boundary flux

      (source code)

      We consider two test problems.

      Testproblem A: Consider in $\Omega_1=(0,1)$

      \[- d_1 \Delta u_1 + k_1 u_1 = c_1\]

      in with homogeneous Neumann boundary conditions.

      Testproblem B: Consider in \Omega_2=(0,1) x (0, 1) $

      \[- d_2 \Delta u_2 + k_2 u_2 = c_2\]

      in with homogeneous Neumann boundary conditions and at the right boundary, i.e. $ {1} x (0, 1) $

      \[- d_b \Delta v + k_b v = c_b.\]

      If d1 = db, k1 = kb and c1 = cb, then u and v should coincide.

      module Example230_BoundaryFlux
+103: Boundary flux · VoronoiFVM.jl
      103: Boundary flux
      (source code)
      We consider two test problems.
      Testproblem A: Consider in $\Omega_1=(0,1)$
      \[- d_1 \Delta u_1  + k_1 u_1 = c_1\]
      in  with homogeneous Neumann boundary conditions.
      Testproblem B: Consider in \Omega_2=(0,1) x (0, 1) $
      \[- d_2 \Delta u_2  + k_2 u_2 = c_2\]
      in  with homogeneous Neumann boundary conditions and at the right boundary, i.e. $ {1} x (0, 1) $
      \[- d_b \Delta v  + k_b v = c_b.\]
      If d1 = db, k1 = kb and c1 = cb, then u and v should coincide.
      module Example230_BoundaryFlux
 
 using VoronoiFVM
 using ExtendableGrids
@@ -144,4 +144,4 @@
         main(; unknown_storage = :sparse, assembly=:cellwise) < 1.0e-14
 end
 
-end # module
      This page was generated using Literate.jl.
      
+end # module

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example301_Laplace3D/index.html b/dev/examples/Example301_Laplace3D/index.html index 1c02cb6a1..610e35244 100644 --- a/dev/examples/Example301_Laplace3D/index.html +++ b/dev/examples/Example301_Laplace3D/index.html @@ -1,5 +1,5 @@ -301: 3D Laplace equation · VoronoiFVM.jl
      Edit on GitHub

      301: 3D Laplace equation

      (source code)

      module Example301_Laplace3D
+301: 3D Laplace equation · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example311_HeatEquation_BoundaryDiffusion/index.html b/dev/examples/Example311_HeatEquation_BoundaryDiffusion/index.html index 8566aa964..32b0c8316 100644 --- a/dev/examples/Example311_HeatEquation_BoundaryDiffusion/index.html +++ b/dev/examples/Example311_HeatEquation_BoundaryDiffusion/index.html @@ -1,5 +1,5 @@ -311: Heat Equation with boundary diffusion · VoronoiFVM.jl
      Edit on GitHub

      311: Heat Equation with boundary diffusion

      (source code)

      module Example311_HeatEquation_BoundaryDiffusion
+311: Heat Equation with boundary diffusion · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example405_GenericOperator/index.html b/dev/examples/Example405_GenericOperator/index.html index 855c21f2b..8ba739a88 100644 --- a/dev/examples/Example405_GenericOperator/index.html +++ b/dev/examples/Example405_GenericOperator/index.html @@ -1,5 +1,5 @@ -405: Generic operator · VoronoiFVM.jl
      Edit on GitHub

      405: Generic operator

      (source code)

      Handle an operator which does not fit into the storage/flux/reaction API. This uses automatic sparsity detection.

      module Example405_GenericOperator
+405: Generic operator · VoronoiFVM.jl
      405: Generic operator
      (source code)
      Handle an operator which does not fit into the storage/flux/reaction API. This uses automatic sparsity detection.
      module Example405_GenericOperator
 using Printf
 using VoronoiFVM
 using ExtendableGrids
@@ -69,4 +69,4 @@
         main(; unknown_storage = :dense) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example406_WeirdReaction/index.html b/dev/examples/Example406_WeirdReaction/index.html index d107f9a4c..5f79618c6 100644 --- a/dev/examples/Example406_WeirdReaction/index.html +++ b/dev/examples/Example406_WeirdReaction/index.html @@ -1,5 +1,5 @@ -406: 1D Weird Surface Reaction · VoronoiFVM.jl
      Edit on GitHub

      406: 1D Weird Surface Reaction

      (source code)

      Species $A$ and $B$ exist in the interior of the domain, species $C$ lives a the boundary $\Gamma_1$. We assume a heterogeneous reaction scheme where $A$ reacts to $B$ with a rate depending on $\nabla A$ near the surface

      \[\begin{aligned} +406: 1D Weird Surface Reaction · VoronoiFVM.jl

      406: 1D Weird Surface Reaction

      (source code)

      Species $A$ and $B$ exist in the interior of the domain, species $C$ lives a the boundary $\Gamma_1$. We assume a heterogeneous reaction scheme where $A$ reacts to $B$ with a rate depending on $\nabla A$ near the surface

      \[\begin{aligned} A &\leftrightarrow B\\ \end{aligned}\]

      In $\Omega$, both $A$ and $B$ are transported through diffusion:

      \[\begin{aligned} \partial_t u_B - \nabla\cdot D_A \nabla u_A & = f_A\\ @@ -154,4 +154,4 @@ main(; unknown_storage = :dense, autodetect_sparsity = false) ≈ testval end -end

      This page was generated using Literate.jl.

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example410_ManySpecies/index.html b/dev/examples/Example410_ManySpecies/index.html index 7edcb7cba..0b715d0af 100644 --- a/dev/examples/Example410_ManySpecies/index.html +++ b/dev/examples/Example410_ManySpecies/index.html @@ -1,5 +1,5 @@ -410: Many Species · VoronoiFVM.jl
      Edit on GitHub

      410: Many Species

      (source code)

      Test stationary diffusion for 50 species.

      module Example410_ManySpecies
+410: Many Species · VoronoiFVM.jl
      410: Many Species
      (source code)
      Test stationary diffusion for 50 species.
      module Example410_ManySpecies
 using Printf
 using VoronoiFVM
 using SparseArrays
@@ -34,4 +34,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example420_DiscontinuousQuantities/index.html b/dev/examples/Example420_DiscontinuousQuantities/index.html index 434348b1f..6174596fc 100644 --- a/dev/examples/Example420_DiscontinuousQuantities/index.html +++ b/dev/examples/Example420_DiscontinuousQuantities/index.html @@ -1,5 +1,5 @@ -420: Discontinuous Quantities · VoronoiFVM.jl
      Edit on GitHub

      420: Discontinuous Quantities

      (source code)

      Test jumping species and quantity handling

      module Example420_DiscontinuousQuantities
+420: Discontinuous Quantities · VoronoiFVM.jl
      420: Discontinuous Quantities
      (source code)
      Test  jumping species and quantity handling
      module Example420_DiscontinuousQuantities
 using Printf
 using VoronoiFVM
 using SparseArrays
@@ -115,4 +115,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example421_AbstractQuantities_TestFunctions/index.html b/dev/examples/Example421_AbstractQuantities_TestFunctions/index.html index e284deab9..494f0aaf4 100644 --- a/dev/examples/Example421_AbstractQuantities_TestFunctions/index.html +++ b/dev/examples/Example421_AbstractQuantities_TestFunctions/index.html @@ -1,5 +1,5 @@ -421: Current Calculation for AbstractQuantities · VoronoiFVM.jl
      Edit on GitHub

      421: Current Calculation for AbstractQuantities

      (source code)

      Test current calculation for jumping species. Here, we have three cases: a. Problem initialized as usual b. Problem initialized with Continuousquantity c. Problem initialized with Discontinuousquantity with adjusted reaction rate We see that the resulting current coincides for all three cases when adjusting the reaction rate.

      module Example421_AbstractQuantities_TestFunctions
+421: Current Calculation for AbstractQuantities · VoronoiFVM.jl
      421: Current Calculation for AbstractQuantities
      (source code)
      Test current calculation for jumping species. Here, we have three cases:     a. Problem initialized as usual     b. Problem initialized with Continuousquantity     c. Problem initialized with Discontinuousquantity with adjusted reaction rate We see that the resulting current coincides for all three cases when adjusting the reaction rate.
      module Example421_AbstractQuantities_TestFunctions
 
 using Printf
 using VoronoiFVM
@@ -143,4 +143,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example422_InterfaceQuantities/index.html b/dev/examples/Example422_InterfaceQuantities/index.html index b39904841..f485740b7 100644 --- a/dev/examples/Example422_InterfaceQuantities/index.html +++ b/dev/examples/Example422_InterfaceQuantities/index.html @@ -1,5 +1,5 @@ -422: Drift-Diffusion with Discontinuous and Interface Potentials · VoronoiFVM.jl
      Edit on GitHub

      422: Drift-Diffusion with Discontinuous and Interface Potentials

      (source code)

      Nondimensionalized semiconductor device equations (with artificial doping) with Discontinuousquantities and additional Interfacequantities.

      module Example422_InterfaceQuantities
+422: Drift-Diffusion with Discontinuous and Interface Potentials · VoronoiFVM.jl
      422: Drift-Diffusion with Discontinuous and Interface Potentials
      (source code)
      Nondimensionalized semiconductor device equations (with artificial doping) with Discontinuousquantities and additional Interfacequantities.
      module Example422_InterfaceQuantities
 
 using VoronoiFVM
 using ExtendableGrids
@@ -202,4 +202,4 @@
         main(; unknown_storage = :dense, assembly=:cellwise) ≈ testval
 end
 
-end # module
      This page was generated using Literate.jl.
      
+end # module

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example424_AbstractQuantitiesInit/index.html b/dev/examples/Example424_AbstractQuantitiesInit/index.html index eec0ad0dd..27f492db8 100644 --- a/dev/examples/Example424_AbstractQuantitiesInit/index.html +++ b/dev/examples/Example424_AbstractQuantitiesInit/index.html @@ -1,5 +1,5 @@ -424: Initialization of Abstract quantities · VoronoiFVM.jl
      Edit on GitHub

      424: Initialization of Abstract quantities

      (source code)

      module Example424_AbstractQuantitiesInit
+424: Initialization of Abstract quantities · VoronoiFVM.jl
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example430_ParameterDerivativesStationary/index.html b/dev/examples/Example430_ParameterDerivativesStationary/index.html index 916796356..e36bca62a 100644 --- a/dev/examples/Example430_ParameterDerivativesStationary/index.html +++ b/dev/examples/Example430_ParameterDerivativesStationary/index.html @@ -1,5 +1,5 @@ -430: Parameter Derivatives (stationary) · VoronoiFVM.jl
      Edit on GitHub

      430: Parameter Derivatives (stationary)

      (source code)

      Explore different ways to calculate sensitivities. This is still experimental.

      module Example430_ParameterDerivativesStationary
+430: Parameter Derivatives (stationary) · VoronoiFVM.jl
      430: Parameter Derivatives (stationary)
      (source code)
      Explore different ways to calculate sensitivities. This is still experimental.
      module Example430_ParameterDerivativesStationary
 
 using VoronoiFVM, ExtendableGrids
 using GridVisualize
@@ -217,4 +217,4 @@
         xg ≈ testval &&
        xg2 ≈ testval &&
              xh ≈ testval
 end
 
-end
      This page was generated using Literate.jl.
      
+end

      This page was generated using Literate.jl.

      diff --git a/dev/examples/Example510_Mixture/index.html b/dev/examples/Example510_Mixture/index.html index b7ed07567..d6eccacd8 100644 --- a/dev/examples/Example510_Mixture/index.html +++ b/dev/examples/Example510_Mixture/index.html @@ -1,5 +1,5 @@ -510: Mixture · VoronoiFVM.jl
      Edit on GitHub

      510: Mixture

      (source code)

      Test mixture diffusion flux. The problem is here that in the flux function we need to solve a linear system of equations which calculates the fluxes from the gradients.# To do so without (heap) allocations can be achieved using StrideArrays, together with the possibility to have static (compile time) information about the size of the local arrays to be allocated.

      $u_i$ are the species partial pressures, $\vec N_i$ are the species fluxes. $D_i^K$ are the Knudsen diffusion coefficients, and $D^B_{ij}$ are the binary diffusion coefficients.

      \[ -\nabla \cdot \vec N_i =0 \quad (i=1\dots n)\\ +510: Mixture · VoronoiFVM.jl

      510: Mixture

      (source code)

      Test mixture diffusion flux. The problem is here that in the flux function we need to solve a linear system of equations which calculates the fluxes from the gradients.# To do so without (heap) allocations can be achieved using StrideArrays, together with the possibility to have static (compile time) information about the size of the local arrays to be allocated.

      $u_i$ are the species partial pressures, $\vec N_i$ are the species fluxes. $D_i^K$ are the Knudsen diffusion coefficients, and $D^B_{ij}$ are the binary diffusion coefficients.

      \[ -\nabla \cdot \vec N_i =0 \quad (i=1\dots n)\\ \frac{\vec N_i}{D^K_i} + \sum_{j\neq i}\frac{u_j \vec N_i - u_i \vec N_j}{D^B_{ij}} = -\vec \nabla u_i \quad (i=1\dots n)\]

      From this representation, we can derive the matrix $M=(m_{ij})$ with

      \[m_{ii}= \frac{1}{D^K_i} + \sum_{j\neq i} \frac{u_j}{D_ij}\\ m_{ij}= -\sum_{j\neq i} \frac{u_i}{D_ij}\]

      such that

      \[ M\begin{pmatrix} \vec N_1\\ @@ -199,4 +199,4 @@ res1 && res2 end -end

      This page was generated using Literate.jl.

      +end

      This page was generated using Literate.jl.

      diff --git a/dev/grid/index.html b/dev/grid/index.html index 907fb9cae..fa4b995d6 100644 --- a/dev/grid/index.html +++ b/dev/grid/index.html @@ -1,2 +1,2 @@ -Grid · VoronoiFVM.jl
      Edit on GitHub
      +Grid · VoronoiFVM.jl
      diff --git a/dev/index.html b/dev/index.html index 720dea504..fd406a738 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Home · VoronoiFVM.jl
      Edit on GitHub

      VoronoiFVM.jl

      Build status DOI Zulip Chat

      Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and DiffResults.jl to evaluate user functions along with their jacobians and calculate derivatives of solutions with respect to their parameters.

      Recent changes

      Please look up the list of recent changes for some breaking changes

      Accompanying packages

      VoronoiFVM.jl and most of these packages are part of the meta package PDELib.jl.

      Some alternatives

      Citation

      If you use this package in your work, please cite it according to CITATION.cff

      +Home · VoronoiFVM.jl

      VoronoiFVM.jl

      Build status DOI Zulip Chat

      Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and DiffResults.jl to evaluate user functions along with their jacobians and calculate derivatives of solutions with respect to their parameters.

      Recent changes

      Please look up the list of recent changes for some breaking changes

      Accompanying packages

      VoronoiFVM.jl and most of these packages are part of the meta package PDELib.jl.

      Some alternatives

      Citation

      If you use this package in your work, please cite it according to CITATION.cff

      diff --git a/dev/internal/index.html b/dev/internal/index.html index 49dd4f17a..186f3d029 100644 --- a/dev/internal/index.html +++ b/dev/internal/index.html @@ -1,32 +1,32 @@ -Internal API · VoronoiFVM.jl
      Edit on GitHub

      Internal API

      Besides of the interface methods for VoronoiFVMDiffEq, these are not exported and therefore should not be used outside of the package

      Wrapping evaluators for physics callbacks

      VoronoiFVM.ResEvaluator — Type
      struct ResEvaluator{Tv<:Number, Func<:Function, G} <: VoronoiFVM.AbstractEvaluator

      Evaluator for functions from physics. Allows to call different types of physic functions (flux, reaction, source) an provides a common interface to different function formats (with data, without data etc.)

      • fwrap::Function: wrapper function in Format ready for Diffetential equations

      • y::Vector{Tv} where Tv<:Number: pre-allocated result

      • geom::Any: Geometry object # geometry (node, edge...)

      • nspec::Int64: number of species

      • isnontrivial::Bool: Is the function not one of nofunc ot nofunc2

      source
      VoronoiFVM.ResEvaluator — Method
       ResEvaluator(physics,symb,uproto,geom,nspec)

      Constructor for ResEvaluator

      • physics Physics object
      • symb: symbol naming one of the functions in physics to be wrapped.
      • uproto: solution vector prototype,
      • geom: node, edge...
      • nspec: number of species
      source
      VoronoiFVM.evaluate! — Method
      evaluate!(e::VoronoiFVM.ResEvaluator)
-

      Call function in evaluator, store result in predefined memory.

      source
      VoronoiFVM.evaluate! — Method
      evaluate!(e::VoronoiFVM.ResEvaluator, u)
-

      Call function in evaluator, store result in predefined memory.

      source
      VoronoiFVM.res — Method
      res(
+Internal API · VoronoiFVM.jl
      Internal API
      Besides of the interface methods for VoronoiFVMDiffEq,  these are not exported and therefore should not be used outside of the package
      Wrapping evaluators for physics callbacks
      VoronoiFVM.ResEvaluator — Type
      struct ResEvaluator{Tv<:Number, Func<:Function, G} <: VoronoiFVM.AbstractEvaluator
      Evaluator for functions from physics. Allows to call different types of physic functions (flux, reaction, source) an provides  a common interface to different function formats (with data, without data etc.)
      • fwrap::Function:  wrapper function in Format ready for Diffetential equations
      • y::Vector{Tv} where Tv<:Number:  pre-allocated result
      • geom::Any:  Geometry object # geometry (node, edge...)
      • nspec::Int64:  number of species
      • isnontrivial::Bool:  Is the  function not one of nofunc ot nofunc2
      source
      VoronoiFVM.ResEvaluator — Method
       ResEvaluator(physics,symb,uproto,geom,nspec)
      Constructor for ResEvaluator
      • physics Physics object
      • symb: symbol naming one of the functions in physics to be wrapped.
      • uproto: solution vector prototype,
      • geom: node, edge...
      • nspec: number of species
      source
      VoronoiFVM.evaluate! — Method
      evaluate!(e::VoronoiFVM.ResEvaluator)
+
      Call function in evaluator, store result in predefined memory.
      source
      VoronoiFVM.evaluate! — Method
      evaluate!(e::VoronoiFVM.ResEvaluator, u)
+
      Call function in evaluator, store result in predefined memory.
      source
      VoronoiFVM.res — Method
      res(
     e::VoronoiFVM.ResEvaluator
 ) -> Vector{Tv} where Tv<:Number
-
      Retrieve evaluation result
      source
      VoronoiFVM.ResJacEvaluator — Type
      struct ResJacEvaluator{Tv<:Number, Func<:Function, Cfg, Res, G} <: VoronoiFVM.AbstractEvaluator
      Evaluator for functions from physics and their Jacobians. Allows to call different types of physic functions (flux, reaction, source) an provides  a common interface to different function formats (with data, without data etc.)
      • fwrap::Function:  wrapper function in Format ready for Differential equations
      • config::Any:  ForwardDiff.JacobianConfig
      • result::Any:  DiffResults.JacobianResult
      • y::Vector{Tv} where Tv<:Number:  pre-allocated result
      • geom::Any:  Geometry object # geometry (node, edge...)
      • nspec::Int64:  number of species
      • isnontrivial::Bool:  Is the  function not one of nofunc ot nofunc2
      source
      VoronoiFVM.ResJacEvaluator — Method
      ResJacEvaluator(physics, symb, uproto, geom, nspec)
-
      Constructor for ResJEvaluator
      • physics Physics object
      • symb: symbol naming one of the functions in physics to be wrapped.
      • uproto: solution vector prototype,
      • geom: node, edge...
      • nspec: number of species
      source
      VoronoiFVM.evaluate! — Method
      evaluate!(e::VoronoiFVM.ResJacEvaluator, u)
-
      Call function in evaluator, store result and jacobian in predefined memory.
      source
      VoronoiFVM.res — Method
      res(e::VoronoiFVM.ResJacEvaluator) -> Any
-
      Retrieve evaluation result
      source
      VoronoiFVM.isnontrivial — Function
      isnontrivial(e::VoronoiFVM.AbstractEvaluator) -> Any
-
      Does calling the evaluator giva nontrivial (nonzero) result?
      source
      Global node and edge assembly loops
      VoronoiFVM.CellwiseAssemblyData — Type
      struct CellwiseAssemblyData{Tv, Ti} <: VoronoiFVM.AbstractAssemblyData{Tv, Ti}
      Data for cellwise assembly.
      • nodefactors::Matrix:     Precomputed geometry factors for cell nodes.     This is a ncells x nnodes_per_cell full matrix.
      • edgefactors::Matrix:     Precomputed geometry factors for cell edges     This is a ncells x nedge_per_cell full matrix.
      source
      VoronoiFVM.EdgewiseAssemblyData — Type
      struct EdgewiseAssemblyData{Tv, Ti} <: VoronoiFVM.AbstractAssemblyData{Tv, Ti}
      • nodefactors::SparseArrays.SparseMatrixCSC{Tv, Ti} where {Tv, Ti}:     Precomputed geometry factors for  nodes.     This is a nnodes x nregions sparse matrix.
      • edgefactors::SparseArrays.SparseMatrixCSC{Tv, Ti} where {Tv, Ti}: Precomputed geometry factors for  edges     This is a nedges x nregions sparse matrix.
      source
      Missing docstring.
      Missing docstring for VoronoiFVM.nodebatch. Check Documenter's build log for details.
      VoronoiFVM.ResJacEvaluator — Type
      struct ResJacEvaluator{Tv<:Number, Func<:Function, Cfg, Res, G} <: VoronoiFVM.AbstractEvaluator
      Evaluator for functions from physics and their Jacobians. Allows to call different types of physic functions (flux, reaction, source) an provides  a common interface to different function formats (with data, without data etc.)
      • fwrap::Function:  wrapper function in Format ready for Differential equations
      • config::Any:  ForwardDiff.JacobianConfig
      • result::Any:  DiffResults.JacobianResult
      • y::Vector{Tv} where Tv<:Number:  pre-allocated result
      • geom::Any:  Geometry object # geometry (node, edge...)
      • nspec::Int64:  number of species
      • isnontrivial::Bool:  Is the  function not one of nofunc ot nofunc2
      source
      VoronoiFVM.ResJacEvaluator — Method
      ResJacEvaluator(physics, symb, uproto, geom, nspec)
+
      Constructor for ResJEvaluator
      • physics Physics object
      • symb: symbol naming one of the functions in physics to be wrapped.
      • uproto: solution vector prototype,
      • geom: node, edge...
      • nspec: number of species
      source
      VoronoiFVM.evaluate! — Method
      evaluate!(e::VoronoiFVM.ResJacEvaluator, u)
+
      Call function in evaluator, store result and jacobian in predefined memory.
      source
      VoronoiFVM.res — Method
      res(e::VoronoiFVM.ResJacEvaluator) -> Any
+
      Retrieve evaluation result
      source
      VoronoiFVM.isnontrivial — Function
      isnontrivial(e::VoronoiFVM.AbstractEvaluator) -> Any
+
      Does calling the evaluator giva nontrivial (nonzero) result?
      source
      Global node and edge assembly loops
      VoronoiFVM.CellwiseAssemblyData — Type
      struct CellwiseAssemblyData{Tv, Ti} <: VoronoiFVM.AbstractAssemblyData{Tv, Ti}
      Data for cellwise assembly.
      • nodefactors::Matrix:     Precomputed geometry factors for cell nodes.     This is a ncells x nnodes_per_cell full matrix.
      • edgefactors::Matrix:     Precomputed geometry factors for cell edges     This is a ncells x nedge_per_cell full matrix.
      source
      VoronoiFVM.EdgewiseAssemblyData — Type
      struct EdgewiseAssemblyData{Tv, Ti} <: VoronoiFVM.AbstractAssemblyData{Tv, Ti}
      • nodefactors::SparseArrays.SparseMatrixCSC{Tv, Ti} where {Tv, Ti}:     Precomputed geometry factors for  nodes.     This is a nnodes x nregions sparse matrix.
      • edgefactors::SparseArrays.SparseMatrixCSC{Tv, Ti} where {Tv, Ti}: Precomputed geometry factors for  edges     This is a nedges x nregions sparse matrix.
      source
      Missing docstring.
      Missing docstring for VoronoiFVM.nodebatch. Check Documenter's build log for details.
      VoronoiFVM._fill! — Function
      _fill!(node, asmdata, inode, icell)
 
      Fill node with the help of assemblydata.
      source
      _fill!(node, asmdata, ibnode, ibface)
 
      Fill boundary node with the help of assemblydata.
      source
      _fill!(edge, asmdata, iedge, icell)
 
      Fill edge with the help of assemblydata.
      source
      _fill!(bedge, asmdata, ibedge, ibface)
 
      Fill boundary edge with the help of assemblydata.
      source
      _fill!(node, asmdata, k, inode)
 
      Fill node with the help of assemblydata.
      source
      _fill!(edge, asmdata, k, iedge)
-
      Fill edge with the help of assemblydata.
      source
      Local node and edge assembly loops
      Local assembly methods organize the assembly of data to those degrees of freedom (dofs) which are defined for a given node or edge. E.g. for an node residual for nspec defined species, only those entries need to be assembled into the global residual vector which correspond to actually defined degrees of freedom. 
      Similarly for  nspec x nspec node Jacobian, an for the nparam x nspec parameter derivatives.
      These local assembly methods organize the correct loops and call back to the concrete assembly methods passed to them. These receive global degrees of freedom and the local species numbers to be handled. The callbacks can be used as well for other purposes than assembly
      Local node and edge assembly loops
      Local assembly methods organize the assembly of data to those degrees of freedom (dofs) which are defined for a given node or edge. E.g. for an node residual for nspec defined species, only those entries need to be assembled into the global residual vector which correspond to actually defined degrees of freedom. 
      Similarly for  nspec x nspec node Jacobian, an for the nparam x nspec parameter derivatives.
      These local assembly methods organize the correct loops and call back to the concrete assembly methods passed to them. These receive global degrees of freedom and the local species numbers to be handled. The callbacks can be used as well for other purposes than assembly
      VoronoiFVM.assemble_res_jac — Function
      assemble_res_jac(node, system, asm_res, asm_jac, asm_param)
 
      Assemble residual and jacobian for node functions. Parameters:
      • system: System to be worked with
      • node: node
      • asm_jac(idof,jdof,ispec,jspec): e.g.  assemble entry ispec,jspec of local jacobian into entry idof,jdof of global matrix
      • asm_param(idof,ispec,iparam) shall assemble parameter derivatives
      source
      assemble_res_jac(bnode, system, asm_res, asm_jac, asm_param)
 
      Assemble residual and jacobian for boundary node functions. See assemble_res_jac for more explanations.
      source
      assemble_res_jac(edge, system, asm_res, asm_jac, asm_param)
 
      Assemble residual and jacobian for edge (flux) functions. Parameters:
      • system: System to be worked with
      • node: node
      • asm_res(idofK,idofL,ispec): e.g. assemble local ispec to global degrees of freedom in unknowns
      • asm_jac(idofK,jdofK,idofL,jdofL,ispec,jspec): e.g.  assemble entry ispec,jspec of local jacobian into entry four entries defined by idofK and idofL of global matrix
      • asm_param(idofK,idofL,ispec,iparam) shall assemble parameter derivatives
      source
      assemble_res_jac(bedge, system, asm_res, asm_jac, asm_param)
-
      Assemble residual and jacobian for boundary edge (flux) functions. See assemble_res_jac for more explanations.
      source
      VoronoiFVM.assemble_res — Function
      assemble_res(node, system, asm_res)
 
      Assemble residual for node functions. See assemble_res_jac for more explanations.
      source
      assemble_res(bnode, system, asm_res)
 
      Assemble residual for boundary node functions. See assemble_res_jac for more explanations.
      source
      assemble_res(edge, system, asm_res)
 
      Assemble residual for edge (flux) functions. See assemble_res_jac for more explanations.
      source
      assemble_res(bedge, system, asm_res)
-
      Assemble residual for boundary edge (flux) functions. See assemble_res_jac for more explanations.
      source
      Degree of Freedom management
      We distinguish
      • active degrees of freedom: these are the actual degrees of freedom 
      • degrees of freedom (dof)  potential degrees of freedom - the may be active dofs or dummy ones With sparse arrays there are no dummy ones, with dense arrays dummy are maske in the node_dof field
      • species: each degree of freedom has associated the species it represents and the node index where it is localized  
      VoronoiFVM.getnodedof — Function
      getnodedof(system,ispec,inode)
      Get active or dummy degree of freedom associated with node and species
      source
      Abstract geometry data
      VoronoiFVM.AbstractNode — Type
      abstract type AbstractNode{Tc<:Number, Tp<:Number, Ti<:Integer} <: VoronoiFVM.AbstractGeometryItem{Tc<:Number, Tp<:Number, Ti<:Integer}
      Abstract type for nodes. 
      node[idim] gives the the corresponding coordinate.
      source
      VoronoiFVM.AbstractNodeData — Type
      abstract type AbstractNodeData{Tv<:Number} <: AbstractArray{Tv<:Number, 1}
      Abstract type for data on nodes. u[ispec] accesses value of species at this node.
      source
      VoronoiFVM.AbstractEdge — Type
      abstract type AbstractEdge{Tv<:Number, Tp<:Number, Ti<:Integer} <: VoronoiFVM.AbstractGeometryItem{Tv<:Number, Tp<:Number, Ti<:Integer}
      Abstract type for edges 
      edge[idim,inode] gives coordinate of node.
      source
      VoronoiFVM.AbstractEdgeData — Type
      abstract type AbstractEdgeData{Tv<:Number} <: AbstractArray{Tv<:Number, 2}
      Abstract type for data on edges. u[ispec,inode] accesses value of species at corresponding node.
      source
      Global assembly & helpers
      Degree of Freedom management
      We distinguish
      • active degrees of freedom: these are the actual degrees of freedom 
      • degrees of freedom (dof)  potential degrees of freedom - the may be active dofs or dummy ones With sparse arrays there are no dummy ones, with dense arrays dummy are maske in the node_dof field
      • species: each degree of freedom has associated the species it represents and the node index where it is localized  
      VoronoiFVM.getnodedof — Function
      getnodedof(system,ispec,inode)
      Get active or dummy degree of freedom associated with node and species
      source
      Abstract geometry data
      VoronoiFVM.AbstractNode — Type
      abstract type AbstractNode{Tc<:Number, Tp<:Number, Ti<:Integer} <: VoronoiFVM.AbstractGeometryItem{Tc<:Number, Tp<:Number, Ti<:Integer}
      Abstract type for nodes. 
      node[idim] gives the the corresponding coordinate.
      source
      VoronoiFVM.AbstractNodeData — Type
      abstract type AbstractNodeData{Tv<:Number} <: AbstractArray{Tv<:Number, 1}
      Abstract type for data on nodes. u[ispec] accesses value of species at this node.
      source
      VoronoiFVM.AbstractEdge — Type
      abstract type AbstractEdge{Tv<:Number, Tp<:Number, Ti<:Integer} <: VoronoiFVM.AbstractGeometryItem{Tv<:Number, Tp<:Number, Ti<:Integer}
      Abstract type for edges 
      edge[idim,inode] gives coordinate of node.
      source
      VoronoiFVM.AbstractEdgeData — Type
      abstract type AbstractEdgeData{Tv<:Number} <: AbstractArray{Tv<:Number, 2}
      Abstract type for data on edges. u[ispec,inode] accesses value of species at corresponding node.
      source
      Global assembly & helpers
      VoronoiFVM.eval_and_assemble — Function
      eval_and_assemble(
     system,
     U,
     UOld,
@@ -37,12 +37,12 @@
     params;
     edge_cutoff
 )
-
      Main assembly method.
      Evaluate solution with result in right hand side F and  assemble Jacobi matrix into system.matrix.
      source
      VoronoiFVM._add — Function
      _add(U::Array{Tv, 2}, idof, val) -> Any
+
      Main assembly method.
      Evaluate solution with result in right hand side F and  assemble Jacobi matrix into system.matrix.
      source
      VoronoiFVM._add — Function
      _add(U::Array{Tv, 2}, idof, val) -> Any
 
      Add residual value into global degree of freedom
      source
      _add(U::VoronoiFVM.SparseSolutionArray, idof, val) -> Any
-
      Add residual value into global degree of freedom
      source
      Interface methods for VoronoiFVMDiffEq.jl
      VoronoiFVM._eval_res_jac! — Function
      _eval_res_jac!(sys, u, t)
-
      Evaluate functiaon and Jacobian at u if they have not been evaluated before at u. See https://github.com/SciML/DifferentialEquations.jl/issues/521 for discussion of another way to do this.
      source
      VoronoiFVM.eval_rhs! — Function
      eval_rhs!(du, u, sys, t)
-
      Interpret the  discrete problem as an ODE/DAE problem. Provide the  rhs function for DifferentialEquations.jl.
      source
      VoronoiFVM.eval_jacobian! — Function
      eval_jacobian!(J, u, sys, t)
-
      Interpret the  discrete problem as an ODE/DAE problem. Provide the  jacobi matrix calculation function for DifferentialEquations.jl.
      source
      VoronoiFVM.mass_matrix — Function
      mass_matrix(system)
-
      Calculate the mass matrix for use with DifferentialEquations.jl. Return a Diagonal matrix if it occurs to be diagonal, otherwise return a SparseMatrixCSC.
      source
      VoronoiFVM.prepare_diffeq! — Function
      prepare_diffeq!(sys, jacval, tjac)
-
      Prepare system for use with VoronoiFVMDiffEq.
      • jacval: value at which to evaluate jacobian to obtatin prototype
      • tjac: time moment for jacobian
      Returns a prototype for the jacobian.
      source
      
+

      Add residual value into global degree of freedom

      source

      Interface methods for VoronoiFVMDiffEq.jl

      VoronoiFVM._eval_res_jac! — Function
      _eval_res_jac!(sys, u, t)
+

      Evaluate functiaon and Jacobian at u if they have not been evaluated before at u. See https://github.com/SciML/DifferentialEquations.jl/issues/521 for discussion of another way to do this.

      source
      VoronoiFVM.eval_rhs! — Function
      eval_rhs!(du, u, sys, t)
+

      Interpret the discrete problem as an ODE/DAE problem. Provide the rhs function for DifferentialEquations.jl.

      source
      VoronoiFVM.eval_jacobian! — Function
      eval_jacobian!(J, u, sys, t)
+

      Interpret the discrete problem as an ODE/DAE problem. Provide the jacobi matrix calculation function for DifferentialEquations.jl.

      source
      VoronoiFVM.mass_matrix — Function
      mass_matrix(system)
+

      Calculate the mass matrix for use with DifferentialEquations.jl. Return a Diagonal matrix if it occurs to be diagonal, otherwise return a SparseMatrixCSC.

      source
      VoronoiFVM.prepare_diffeq! — Function
      prepare_diffeq!(sys, jacval, tjac)
+

      Prepare system for use with VoronoiFVMDiffEq.

      • jacval: value at which to evaluate jacobian to obtatin prototype
      • tjac: time moment for jacobian

      Returns a prototype for the jacobian.

      source
      diff --git a/dev/method/index.html b/dev/method/index.html index 90b19da5b..d89d10825 100644 --- a/dev/method/index.html +++ b/dev/method/index.html @@ -1,5 +1,5 @@ -The Voronoi finite volume method · VoronoiFVM.jl
      Edit on GitHub

      The Voronoi finite volume method

      Construction of control volumes

      • Start with a boundary conforming Delaunay triangulation of a polygonal domain (intervals in 1D, triangles in 2D, tetrahedra in 3D). Such a triangulation can be generated by e.g. by the mesh generators triangle and TetGen. These are available in Julia via Triangulate.jl and TetGen.jl. For simple geometries – tensor products of lower dimensional grids – such triangulation can be created more easily. The package ExtendableGrids.jl manages the grid data structure which is used in this package. SimplexGridFactory.jl interfaces this grid structure with Triangulate.jl and TetGen.jl and provides an API for incrementally setting up geometry descriptions.

      • Join triangle circumcenters by lines $\rightarrow$ create Voronoi cells which can serve as control volumes, akin to representative elementary volumes (REV) used to derive conservation laws.

      +The Voronoi finite volume method · VoronoiFVM.jl

      The Voronoi finite volume method

      Construction of control volumes

      • Start with a boundary conforming Delaunay triangulation of a polygonal domain (intervals in 1D, triangles in 2D, tetrahedra in 3D). Such a triangulation can be generated by e.g. by the mesh generators triangle and TetGen. These are available in Julia via Triangulate.jl and TetGen.jl. For simple geometries – tensor products of lower dimensional grids – such triangulation can be created more easily. The package ExtendableGrids.jl manages the grid data structure which is used in this package. SimplexGridFactory.jl interfaces this grid structure with Triangulate.jl and TetGen.jl and provides an API for incrementally setting up geometry descriptions.

      • Join triangle circumcenters by lines $\rightarrow$ create Voronoi cells which can serve as control volumes, akin to representative elementary volumes (REV) used to derive conservation laws.

      • Black + green: triangle nodes
      • Gray: triangle edges
      • Blue: triangle circumcenters
      • Red: Boundaries of Voronoi cells

      In order to make this construction possible, the triangulation must have the boundary conforming Delaunay property:

      • The interior of any triangle circumcircle does not contain any other node of the triangulation
      • All circumcircle centers lay within the domain

      In 2D, an equivalent condition is:

      • The sum of triangle angles opposite to a given interior edge is less than $\pi$
      • Triangle angles opposite to boundary edges are less than $\frac\pi2$.

      As a consequence, there is a 1:1 incidence between triangulation nodes and Voronoi cells. Moreover, the angle between the interface between two neighboring Voronoi cells and the edge between their corresponding nodes is $\frac\pi2$. Therefore the edge direction is aligned with the normal direction with respect to the boundary of the Voronoi cell. This makes it easy to use these Voronoi cells as REVs aka control volumes aka finite volume cells and to derive a space discretization for a conservation law based on very same balance rules used to derive this conservation law.

      The discretization approach

      @@ -18,4 +18,4 @@ \text{boundary terms}&=\sum_{m\in\mathcal M_k} \int_{\gamma_{km}} \vec j \cdot \vec n d s &\approx \sum_{m\in\mathcal M_k} |\gamma_{km}| \vec j \cdot \vec n\\ &\approx\sum_{m\in\mathcal M_k} |\gamma_{km}| (au_k -b), -\end{aligned}\]

      We observe that for $\varepsilon\to 0$, the Robin boundary condition

      \[- \vec j \cdot \vec n + \frac{1}{\varepsilon}u = \frac{1}{\varepsilon}g\]

      tends to the Dirichlet bundary condition

      \[ u=g.\]

      Therefore, a Dirichlet boundary condition can be approximated by choosing a small value of $\varepsilon$ and implying the aforementioned Robin boundary conditions. This approach called penalty method is chosen for the implementation of Dirichlet boundary conditions in this package.

      Time dependent problems, reaction terms

      This approach easily generalizes to time dependent nonlinear transport-reaction problems with storage terms $s(u)$, reaction terms $r(u)$ and source terms $f$:

      \[\partial_t s(u) + \nabla \cdot \vec j + r(u) -f =0\]

      Semidiscretization in time (for implicit Euler) leads to

      \[\frac{s(u)-s(u^\flat)}{\tau} + \nabla \cdot \vec j + r(u) -f =0\]

      where $\tau$ is the time step size and $u^\flat$ is the solution from the old timestep. The approximation approach then for each control volume gives

      \[|\omega_k|\frac{s(u_k)-s(u_k^\flat)}{\tau} + \sum_{l\in N_k} \frac{\sigma_{kl}}{h_{kl}}g(u_k, u_l)+ \sum_{m\in\mathcal M_k} |\gamma_{km}| (au_k -b) + |\omega_k| (r(u_k)- f_k)=0\]

      If $n$ is the number of discretization nodes, we get a system of $n$ equations with $n$ unknowns which under proper conditions on $r,g,s$ has a unique solution.

      The implicit Euler method is the default solver for time dependent problems. Alternatively, ODE and DAE solvers from DifferentialEquations.jl can be used with an upcoming glue package.

      Generalizations to systems

      This approach generalizes to systems of partial differential equations, which formally can be written in the same way, but assuming that $u$ is a vector function of $\vec x,t$, and $r,g,s$ are vector functions of their arguments. The package allows to handle different sets of species in different subdomains of $\Omega$.

      Boundary reactions, boundary species

      In addition to $r,g,s$, the package allows to specify additional boundary species, boundary reaction, boundary flux and boundary storage terms.

      Why this method ?

      Independent of space dimension, the method (with properly chosen flux functions) is able to preserve a number of physical quantities if they are present on the continuous level:

      • local and global mass conservation
      • positivity of solutions
      • maximum principle: in the absence of source and reaction terms, local extrema of the stationary solution are located at the domain boundaries, never in the interior. For transient problems, local extrema in the interior can only come from the initial value.
      • Consistency to thermodynamics: entropy production etc.

      Many of these properties are hard to prove for finite element methods, in particular for the convection-diffusion case.

      Where is this method not appropriate ?

      There are a number of cases where this method needs to be replaced by something else or at least to be applied with great care:

      • Anisotropic diffusion only works with proper mesh alignment
      • Strongly varying capacity (in the function $s$) at domain interfaces lead to inexact breakthrough curves
      • Sharp moving convection fronts are smeared out too strongly

      History and literature

      The following list is work in progress and incomplete, but it references some sources behind the ideas in this package.

      • Macneal, R. H. (1953). An asymmetrical finite difference network. Quarterly of Applied Mathematics, 11(3), 295-310. (pdf via JSTOR). Perhaps this is the earliest mentioning of the method. Note that it was used on an electrical analog computer.
      • Gärtner, K., & Kamenski, L. (2019). Why do we need Voronoi cells and Delaunay meshes? arXiv preprint arXiv:1905.01738. A recent overview on the merits of the method. One of the authors belongs to the pioneers of its application in 3D.
      • Fuhrmann, J., & Langmach, H. (2001). Stability and existence of solutions of time-implicit finite volume schemes for viscous nonlinear conservation laws. Applied Numerical Mathematics, 37(1-2), 201-230. A discussion of the method applied to rather general nonlinear scalar problems.
      • Si, H., Gärtner, K., & Fuhrmann, J. (2010). Boundary conforming Delaunay mesh generation. Computational Mathematics and Mathematical Physics, 50(1), 38-53. Definition of the boundary conforming Delaunay property.
      • Eymard, R., Fuhrmann, J., & Gärtner, K. (2006). A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local Dirichlet problems. Numerische Mathematik, 102(3), 463-495. General concept of the derivation of upwind fluxes for nonlinear problems.
      • Farrell, P., Rotundo, N., Doan, D. H., Kantner, M., Fuhrmann, J., & Koprucki, T. (2017). Drift-diffusion models. In Handbook of Optoelectronic Device Modeling and Simulation (pp. 733-772). CRC Press. Overview and introduction to the method applied to semiconductor device simulation. This problem class profits most from the desirable properties of the method.

      Software API and implementation

      The entities describing the discrete system can be subdivided into two categories:

      • Geometrical data: $|\omega_k|, \gamma_k, \sigma_{kl}, h_{kl}$ together with the connectivity information simplex grid. These data are calculated from the discretization grid.
      • Physics data: the number of species and the functions $s,g,r,f$ etc. describing the particular problem.

      The solution of the nonlinear systems of equations is performed by Newton's method combined with various direct and iterative linear solvers. The Jacobi matrices used in Newton's method are assembled from the constitutive functions with the help of forward mode automatic differentiation implemented in ForwardDiff.jl.

      +\end{aligned}\]

      We observe that for $\varepsilon\to 0$, the Robin boundary condition

      \[- \vec j \cdot \vec n + \frac{1}{\varepsilon}u = \frac{1}{\varepsilon}g\]

      tends to the Dirichlet bundary condition

      \[ u=g.\]

      Therefore, a Dirichlet boundary condition can be approximated by choosing a small value of $\varepsilon$ and implying the aforementioned Robin boundary conditions. This approach called penalty method is chosen for the implementation of Dirichlet boundary conditions in this package.

      Time dependent problems, reaction terms

      This approach easily generalizes to time dependent nonlinear transport-reaction problems with storage terms $s(u)$, reaction terms $r(u)$ and source terms $f$:

      \[\partial_t s(u) + \nabla \cdot \vec j + r(u) -f =0\]

      Semidiscretization in time (for implicit Euler) leads to

      \[\frac{s(u)-s(u^\flat)}{\tau} + \nabla \cdot \vec j + r(u) -f =0\]

      where $\tau$ is the time step size and $u^\flat$ is the solution from the old timestep. The approximation approach then for each control volume gives

      \[|\omega_k|\frac{s(u_k)-s(u_k^\flat)}{\tau} + \sum_{l\in N_k} \frac{\sigma_{kl}}{h_{kl}}g(u_k, u_l)+ \sum_{m\in\mathcal M_k} |\gamma_{km}| (au_k -b) + |\omega_k| (r(u_k)- f_k)=0\]

      If $n$ is the number of discretization nodes, we get a system of $n$ equations with $n$ unknowns which under proper conditions on $r,g,s$ has a unique solution.

      The implicit Euler method is the default solver for time dependent problems. Alternatively, ODE and DAE solvers from DifferentialEquations.jl can be used with an upcoming glue package.

      Generalizations to systems

      This approach generalizes to systems of partial differential equations, which formally can be written in the same way, but assuming that $u$ is a vector function of $\vec x,t$, and $r,g,s$ are vector functions of their arguments. The package allows to handle different sets of species in different subdomains of $\Omega$.

      Boundary reactions, boundary species

      In addition to $r,g,s$, the package allows to specify additional boundary species, boundary reaction, boundary flux and boundary storage terms.

      Why this method ?

      Independent of space dimension, the method (with properly chosen flux functions) is able to preserve a number of physical quantities if they are present on the continuous level:

      • local and global mass conservation
      • positivity of solutions
      • maximum principle: in the absence of source and reaction terms, local extrema of the stationary solution are located at the domain boundaries, never in the interior. For transient problems, local extrema in the interior can only come from the initial value.
      • Consistency to thermodynamics: entropy production etc.

      Many of these properties are hard to prove for finite element methods, in particular for the convection-diffusion case.

      Where is this method not appropriate ?

      There are a number of cases where this method needs to be replaced by something else or at least to be applied with great care:

      • Anisotropic diffusion only works with proper mesh alignment
      • Strongly varying capacity (in the function $s$) at domain interfaces lead to inexact breakthrough curves
      • Sharp moving convection fronts are smeared out too strongly

      History and literature

      The following list is work in progress and incomplete, but it references some sources behind the ideas in this package.

      • Macneal, R. H. (1953). An asymmetrical finite difference network. Quarterly of Applied Mathematics, 11(3), 295-310. (pdf via JSTOR). Perhaps this is the earliest mentioning of the method. Note that it was used on an electrical analog computer.
      • Gärtner, K., & Kamenski, L. (2019). Why do we need Voronoi cells and Delaunay meshes? arXiv preprint arXiv:1905.01738. A recent overview on the merits of the method. One of the authors belongs to the pioneers of its application in 3D.
      • Fuhrmann, J., & Langmach, H. (2001). Stability and existence of solutions of time-implicit finite volume schemes for viscous nonlinear conservation laws. Applied Numerical Mathematics, 37(1-2), 201-230. A discussion of the method applied to rather general nonlinear scalar problems.
      • Si, H., Gärtner, K., & Fuhrmann, J. (2010). Boundary conforming Delaunay mesh generation. Computational Mathematics and Mathematical Physics, 50(1), 38-53. Definition of the boundary conforming Delaunay property.
      • Eymard, R., Fuhrmann, J., & Gärtner, K. (2006). A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local Dirichlet problems. Numerische Mathematik, 102(3), 463-495. General concept of the derivation of upwind fluxes for nonlinear problems.
      • Farrell, P., Rotundo, N., Doan, D. H., Kantner, M., Fuhrmann, J., & Koprucki, T. (2017). Drift-diffusion models. In Handbook of Optoelectronic Device Modeling and Simulation (pp. 733-772). CRC Press. Overview and introduction to the method applied to semiconductor device simulation. This problem class profits most from the desirable properties of the method.

      Software API and implementation

      The entities describing the discrete system can be subdivided into two categories:

      • Geometrical data: $|\omega_k|, \gamma_k, \sigma_{kl}, h_{kl}$ together with the connectivity information simplex grid. These data are calculated from the discretization grid.
      • Physics data: the number of species and the functions $s,g,r,f$ etc. describing the particular problem.

      The solution of the nonlinear systems of equations is performed by Newton's method combined with various direct and iterative linear solvers. The Jacobi matrices used in Newton's method are assembled from the constitutive functions with the help of forward mode automatic differentiation implemented in ForwardDiff.jl.

      diff --git a/dev/misc/index.html b/dev/misc/index.html index 08f9497b7..f31c33bf4 100644 --- a/dev/misc/index.html +++ b/dev/misc/index.html @@ -1,7 +1,7 @@ -Miscellaneous · VoronoiFVM.jl
      Edit on GitHub

      Miscellaneous

      Useful helpers

      VoronoiFVM.value — Function

      Extract value from dual number. Use to debug physics callbacks. Re-exported from ForwardDiff.jl

      source

      Form factor calculatione

      Velocity projections

      Additional grid methods

      VoronoiFVM.Grid — Function
      Grid=ExtendableGrids.simplexgrid

      Re-Export of ExtendableGrids.simplexgrid

      source

      Exception types

      +Miscellaneous · VoronoiFVM.jl

      Miscellaneous

      Useful helpers

      VoronoiFVM.value — Function

      Extract value from dual number. Use to debug physics callbacks. Re-exported from ForwardDiff.jl

      source

      Form factor calculatione

      Velocity projections

      Additional grid methods

      VoronoiFVM.Grid — Function
      Grid=ExtendableGrids.simplexgrid

      Re-Export of ExtendableGrids.simplexgrid

      source

      Exception types

      diff --git a/dev/nbhtml/api-update.html b/dev/nbhtml/api-update.html index 33a2fca84..67556656b 100644 --- a/dev/nbhtml/api-update.html +++ b/dev/nbhtml/api-update.html @@ -1,16 +1,16 @@ - -
      \ No newline at end of file +
      \ No newline at end of file diff --git a/dev/nbhtml/api-update/index.html b/dev/nbhtml/api-update/index.html index 208765a39..f7bfb0514 100644 --- a/dev/nbhtml/api-update/index.html +++ b/dev/nbhtml/api-update/index.html @@ -1,2 +1,2 @@ -API Updates · VoronoiFVM.jl
      Edit on GitHub
      +API Updates · VoronoiFVM.jl
      diff --git a/dev/nbhtml/flux-reconstruction.html b/dev/nbhtml/flux-reconstruction.html index 07ddbf573..67094cd44 100644 --- a/dev/nbhtml/flux-reconstruction.html +++ b/dev/nbhtml/flux-reconstruction.html @@ -1,16 +1,16 @@ - -
      \ No newline at end of file +
      \ No newline at end of file diff --git a/dev/nbhtml/flux-reconstruction/index.html b/dev/nbhtml/flux-reconstruction/index.html index 5823000d2..efc297bae 100644 --- a/dev/nbhtml/flux-reconstruction/index.html +++ b/dev/nbhtml/flux-reconstruction/index.html @@ -1,2 +1,2 @@ -Obtaining vector fields · VoronoiFVM.jl
      Edit on GitHub
      +Obtaining vector fields · VoronoiFVM.jl
      diff --git a/dev/nbhtml/interfaces1d.html b/dev/nbhtml/interfaces1d.html index eaaa449ed..fb2a30ec5 100644 --- a/dev/nbhtml/interfaces1d.html +++ b/dev/nbhtml/interfaces1d.html @@ -1,16 +1,16 @@ - -
      \ No newline at end of file +
      \ No newline at end of file diff --git a/dev/nbhtml/interfaces1d/index.html b/dev/nbhtml/interfaces1d/index.html index 58f731ddc..68cd38281 100644 --- a/dev/nbhtml/interfaces1d/index.html +++ b/dev/nbhtml/interfaces1d/index.html @@ -1,2 +1,2 @@ -Internal interfaces (1D) · VoronoiFVM.jl
      Edit on GitHub
      +Internal interfaces (1D) · VoronoiFVM.jl
      diff --git a/dev/nbhtml/nonlinear-solvers.html b/dev/nbhtml/nonlinear-solvers.html index 87faf35c1..2c3e982bb 100644 --- a/dev/nbhtml/nonlinear-solvers.html +++ b/dev/nbhtml/nonlinear-solvers.html @@ -1,16 +1,16 @@ - -
      \ No newline at end of file +
      \ No newline at end of file diff --git a/dev/nbhtml/nonlinear-solvers/index.html b/dev/nbhtml/nonlinear-solvers/index.html index f4482db02..73265d785 100644 --- a/dev/nbhtml/nonlinear-solvers/index.html +++ b/dev/nbhtml/nonlinear-solvers/index.html @@ -1,2 +1,2 @@ -Nonlinear solver control · VoronoiFVM.jl
      Edit on GitHub
      +Nonlinear solver control · VoronoiFVM.jl
      diff --git a/dev/nbhtml/outflow.html b/dev/nbhtml/outflow.html index 75195a5b0..4ffcdc4da 100644 --- a/dev/nbhtml/outflow.html +++ b/dev/nbhtml/outflow.html @@ -1,16 +1,16 @@ - -
      \ No newline at end of file +
      \ No newline at end of file diff --git a/dev/nbhtml/outflow/index.html b/dev/nbhtml/outflow/index.html index 9d367fb76..2a8c90242 100644 --- a/dev/nbhtml/outflow/index.html +++ b/dev/nbhtml/outflow/index.html @@ -1,2 +1,2 @@ -Outflow boundary conditions · VoronoiFVM.jl
      Edit on GitHub
      +Outflow boundary conditions · VoronoiFVM.jl
      diff --git a/dev/nbhtml/pluto_export.json b/dev/nbhtml/pluto_export.json index e2497658f..3cecf93a5 100644 --- a/dev/nbhtml/pluto_export.json +++ b/dev/nbhtml/pluto_export.json @@ -1 +1 @@ -{"notebooks":{"interfaces1d.jl":{"id":"interfaces1d.jl","hash":"m-n4T9PkfrHCvgS8bUxhOpXTrLuJN2iOTkwc1ywZY-8","html_path":"interfaces1d.html","statefile_path":null,"notebookfile_path":null,"current_hash":"m-n4T9PkfrHCvgS8bUxhOpXTrLuJN2iOTkwc1ywZY-8","desired_hash":"m-n4T9PkfrHCvgS8bUxhOpXTrLuJN2iOTkwc1ywZY-8","frontmatter":{"title":"interfaces1d"}},"outflow.jl":{"id":"outflow.jl","hash":"ngpcZXX2L7p7KDj6VxB2niBalYSt3s65VRYtBnx3Shc","html_path":"outflow.html","statefile_path":null,"notebookfile_path":null,"current_hash":"ngpcZXX2L7p7KDj6VxB2niBalYSt3s65VRYtBnx3Shc","desired_hash":"ngpcZXX2L7p7KDj6VxB2niBalYSt3s65VRYtBnx3Shc","frontmatter":{"title":"outflow"}},"flux-reconstruction.jl":{"id":"flux-reconstruction.jl","hash":"oNsf4h9IJQBzo50ZI0QTZyct0RtM47ayk0q268FOsNc","html_path":"flux-reconstruction.html","statefile_path":null,"notebookfile_path":null,"current_hash":"oNsf4h9IJQBzo50ZI0QTZyct0RtM47ayk0q268FOsNc","desired_hash":"oNsf4h9IJQBzo50ZI0QTZyct0RtM47ayk0q268FOsNc","frontmatter":{"title":"flux-reconstruction"}},"problemcase.jl":{"id":"problemcase.jl","hash":"upSJ6tV_2q3QlQ7CdM58_HZ8Hcc3N2nSRmK6tJW5YzU","html_path":"problemcase.html","statefile_path":null,"notebookfile_path":null,"current_hash":"upSJ6tV_2q3QlQ7CdM58_HZ8Hcc3N2nSRmK6tJW5YzU","desired_hash":"upSJ6tV_2q3QlQ7CdM58_HZ8Hcc3N2nSRmK6tJW5YzU","frontmatter":{"title":"problemcase"}},"api-update.jl":{"id":"api-update.jl","hash":"dLFQVxR-A6LWKJHcudn72yUtnuMeYiQLLUKslpWGEIA","html_path":"api-update.html","statefile_path":null,"notebookfile_path":null,"current_hash":"dLFQVxR-A6LWKJHcudn72yUtnuMeYiQLLUKslpWGEIA","desired_hash":"dLFQVxR-A6LWKJHcudn72yUtnuMeYiQLLUKslpWGEIA","frontmatter":{"title":"api-update"}},"nonlinear-solvers.jl":{"id":"nonlinear-solvers.jl","hash":"rB3Bszi0owOelKMOMDpWIleeCE7uhK922xhPCp_dE_A","html_path":"nonlinear-solvers.html","statefile_path":null,"notebookfile_path":null,"current_hash":"rB3Bszi0owOelKMOMDpWIleeCE7uhK922xhPCp_dE_A","desired_hash":"rB3Bszi0owOelKMOMDpWIleeCE7uhK922xhPCp_dE_A","frontmatter":{"title":"nonlinear-solvers"}}},"pluto_version":"0.19.27","julia_version":"1.9.2","format_version":"1","title":null,"description":null,"collections":null} \ No newline at end of file +{"notebooks":{"interfaces1d.jl":{"id":"interfaces1d.jl","hash":"m-n4T9PkfrHCvgS8bUxhOpXTrLuJN2iOTkwc1ywZY-8","html_path":"interfaces1d.html","statefile_path":null,"notebookfile_path":null,"current_hash":"m-n4T9PkfrHCvgS8bUxhOpXTrLuJN2iOTkwc1ywZY-8","desired_hash":"m-n4T9PkfrHCvgS8bUxhOpXTrLuJN2iOTkwc1ywZY-8","frontmatter":{"title":"interfaces1d"}},"outflow.jl":{"id":"outflow.jl","hash":"ngpcZXX2L7p7KDj6VxB2niBalYSt3s65VRYtBnx3Shc","html_path":"outflow.html","statefile_path":null,"notebookfile_path":null,"current_hash":"ngpcZXX2L7p7KDj6VxB2niBalYSt3s65VRYtBnx3Shc","desired_hash":"ngpcZXX2L7p7KDj6VxB2niBalYSt3s65VRYtBnx3Shc","frontmatter":{"title":"outflow"}},"flux-reconstruction.jl":{"id":"flux-reconstruction.jl","hash":"oNsf4h9IJQBzo50ZI0QTZyct0RtM47ayk0q268FOsNc","html_path":"flux-reconstruction.html","statefile_path":null,"notebookfile_path":null,"current_hash":"oNsf4h9IJQBzo50ZI0QTZyct0RtM47ayk0q268FOsNc","desired_hash":"oNsf4h9IJQBzo50ZI0QTZyct0RtM47ayk0q268FOsNc","frontmatter":{"title":"flux-reconstruction"}},"problemcase.jl":{"id":"problemcase.jl","hash":"upSJ6tV_2q3QlQ7CdM58_HZ8Hcc3N2nSRmK6tJW5YzU","html_path":"problemcase.html","statefile_path":null,"notebookfile_path":null,"current_hash":"upSJ6tV_2q3QlQ7CdM58_HZ8Hcc3N2nSRmK6tJW5YzU","desired_hash":"upSJ6tV_2q3QlQ7CdM58_HZ8Hcc3N2nSRmK6tJW5YzU","frontmatter":{"title":"problemcase"}},"api-update.jl":{"id":"api-update.jl","hash":"dLFQVxR-A6LWKJHcudn72yUtnuMeYiQLLUKslpWGEIA","html_path":"api-update.html","statefile_path":null,"notebookfile_path":null,"current_hash":"dLFQVxR-A6LWKJHcudn72yUtnuMeYiQLLUKslpWGEIA","desired_hash":"dLFQVxR-A6LWKJHcudn72yUtnuMeYiQLLUKslpWGEIA","frontmatter":{"title":"api-update"}},"nonlinear-solvers.jl":{"id":"nonlinear-solvers.jl","hash":"rB3Bszi0owOelKMOMDpWIleeCE7uhK922xhPCp_dE_A","html_path":"nonlinear-solvers.html","statefile_path":null,"notebookfile_path":null,"current_hash":"rB3Bszi0owOelKMOMDpWIleeCE7uhK922xhPCp_dE_A","desired_hash":"rB3Bszi0owOelKMOMDpWIleeCE7uhK922xhPCp_dE_A","frontmatter":{"title":"nonlinear-solvers"}}},"pluto_version":"0.19.32","julia_version":"1.9.3","format_version":"1","title":null,"description":null,"collections":null,"binder_url":null,"slider_server_url":null} \ No newline at end of file diff --git a/dev/nbhtml/problemcase.html b/dev/nbhtml/problemcase.html index dc7ed1985..a21068475 100644 --- a/dev/nbhtml/problemcase.html +++ b/dev/nbhtml/problemcase.html @@ -1,16 +1,16 @@ - -
      \ No newline at end of file +
      \ No newline at end of file diff --git a/dev/nbhtml/problemcase/index.html b/dev/nbhtml/problemcase/index.html index 192f2ba56..2eeb63995 100644 --- a/dev/nbhtml/problemcase/index.html +++ b/dev/nbhtml/problemcase/index.html @@ -1,2 +1,2 @@ -A case for caution · VoronoiFVM.jl
      Edit on GitHub
      +A case for caution · VoronoiFVM.jl
      diff --git a/dev/notebooks/index.html b/dev/notebooks/index.html index e53b87fef..635bcec1d 100644 --- a/dev/notebooks/index.html +++ b/dev/notebooks/index.html @@ -1,2 +1,2 @@ -About the notebooks · VoronoiFVM.jl
      Edit on GitHub

      About the notebooks

      Pluto.jl notebooks provide a great opportunity to put together code, text and graphics in a reproducible and accessible way. Therefore, the examples for this package are being amended by a series of Pluto notebooks. Like the example code, the notebook code is tested during CI.

      The notebooks use an updated and simplified version of the VoronoiFVM API.

      Please note, that in the html version, interactive elements like sliders are disabled. Navigation via the table of contents does work, though.

      +About the notebooks · VoronoiFVM.jl

      About the notebooks

      Pluto.jl notebooks provide a great opportunity to put together code, text and graphics in a reproducible and accessible way. Therefore, the examples for this package are being amended by a series of Pluto notebooks. Like the example code, the notebook code is tested during CI.

      The notebooks use an updated and simplified version of the VoronoiFVM API.

      Please note, that in the html version, interactive elements like sliders are disabled. Navigation via the table of contents does work, though.

      diff --git a/dev/physics/index.html b/dev/physics/index.html index cd05885a0..06bc68a45 100644 --- a/dev/physics/index.html +++ b/dev/physics/index.html @@ -1,5 +1,5 @@ -Physics & special functions · VoronoiFVM.jl
      Edit on GitHub

      Physics & special functions

      Physics

      VoronoiFVM.Physics — Type
      struct Physics

      Physics data record with the following fields:

      • flux::Function: Flux between neighboring control volumes: flux(f,u,edge) or flux(f,u,edge,data) should return in f[i] the flux of species i along the edge joining circumcenters of neighboring control volumes. u is a 2D array such that for species i, u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.

      • storage::Function: Storage term (term under time derivative): storage(f,u,node) or storage(f,u,node,data)

        It should return in f[i] the storage term for the i-th equation. u[i] contains the value of the i-th unknown.

      • reaction::Function: Reaction term: reaction(f,u,node) or reaction(f,u,node,data)

        It should return in f[i] the reaction term for the i-th equation. u[i] contains the value of the i-th unknown.

      • edgereaction::Function: Edge reaction term: edgereaction(f,u,edge) or edgereaction(f,u,edge,data)

        It should return in f[i] the reaction term for the i-th equation. u[i] contains the value of the i-th unknown. u is a 2D array such that for species i, u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.

      • source::Function: Source term: source(f,node) or source(f,node,data).

        It should return the in f[i] the value of the source term for the i-th equation.

      • bflux::Function: Flux between neighboring control volumes on the boundary. Called on edges fully adjacent to the boundary: bflux(f,u,bedge) or `bflux(f,u,bedge,data)
      • breaction::Function: Boundary reaction term: breaction(f,u,node) or breaction(f,u,node,data) Similar to reaction, but restricted to the inner or outer boundaries.

      • bsource::Function: Boundary source term: bsource(f,node) or bsource(f,node,data).

        It should return in f[i] the value of the source term for the i-th equation.

      • bstorage::Function: Boundary storage term: bstorage(f,u,node) or bstorage(f,u,node,data) Similar to storage, but restricted to the inner or outer boundaries.
      • boutflow::Function: Outflow boundary term boutflow(f,u,edge) or boutflow(f,u,edge,data) This function is called for edges (including interior ones) which have at least one ode on one of the outflow boundaries. Within this function, outflownode and isoutflownode can be used to identify that node. There is some ambiguity in the case that both nodes are outflow nodes, in that case it is assumed that the contribution is zero.
      • outflowboundaries::Vector{Int64}: List (Vector) of boundary regions which carry outflow bondary conditions. Influences when boutflow is called.
      • generic_operator::Function: Generic operator generic_operator(f,u,sys). This operator acts on the full solution u of a system. Sparsity is detected automatically unless generic_operator_sparsity is given.
      • generic_operator_sparsity::Function: Function defining the sparsity structure of the generic operator. This should return the sparsity pattern of the generic_operator.
      • data::Any: User data (parameters). This allows to pass various parameters to the callback functions.
      • num_species::Int8: Number of species including boundary species.
      source
      VoronoiFVM.Physics — Method
      Physics(;num_species=0,
+Physics & special functions · VoronoiFVM.jl
      Physics & special functions
      Physics
      VoronoiFVM.Physics — Type
      struct Physics
      Physics data record with the following fields:
      • flux::Function: Flux between neighboring control volumes: flux(f,u,edge) or flux(f,u,edge,data) should return in f[i] the flux of species i along the edge joining circumcenters of neighboring control volumes.  u is a  2D array such that for species i, u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.
      • storage::Function: Storage term (term under time derivative): storage(f,u,node) or storage(f,u,node,data)
        It should return in f[i] the storage term for the i-th equation. u[i] contains the value of the i-th unknown.
      • reaction::Function: Reaction term:  reaction(f,u,node) or reaction(f,u,node,data)
        It should return in f[i] the reaction term for the i-th equation. u[i] contains the value of the i-th unknown.
      • edgereaction::Function: Edge reaction term:  edgereaction(f,u,edge) or edgereaction(f,u,edge,data)
        It should return in f[i] the reaction term for the i-th equation. u[i] contains the value of the i-th unknown.  u is a  2D array such that for species i, u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.
      • source::Function: Source term: source(f,node) or source(f,node,data).
        It should return the in f[i] the value of the source term for the i-th equation.
      • bflux::Function: Flux between neighboring control volumes on the boundary. Called on edges fully adjacent to the boundary: bflux(f,u,bedge) or `bflux(f,u,bedge,data)
      • breaction::Function: Boundary reaction term:  breaction(f,u,node) or breaction(f,u,node,data) Similar to reaction, but restricted to the inner or outer boundaries.
      • bsource::Function: Boundary source term: bsource(f,node) or bsource(f,node,data).
        It should return in f[i] the value of the source term for the i-th equation.
      • bstorage::Function: Boundary storage term: bstorage(f,u,node) or bstorage(f,u,node,data) Similar to storage, but restricted to the inner or outer boundaries.
      • boutflow::Function: Outflow boundary term  boutflow(f,u,edge) or boutflow(f,u,edge,data) This function is called for edges (including interior ones) which have at least one ode on one of the outflow boundaries. Within this function, outflownode and  isoutflownode can be used to identify that node.  There is some ambiguity in the case that both nodes are outflow nodes, in that case it is assumed that the contribution is zero.
      • outflowboundaries::Vector{Int64}: List (Vector) of boundary regions which carry outflow bondary conditions. Influences when boutflow is called.
      • generic_operator::Function: Generic operator  generic_operator(f,u,sys). This operator acts on the full solution u of a system. Sparsity is detected automatically  unless generic_operator_sparsity is given.
      • generic_operator_sparsity::Function: Function defining the sparsity structure of the generic operator. This should return the sparsity pattern of the generic_operator.
      • data::Any: User data (parameters). This allows to pass various parameters to the callback functions.
      • num_species::Int8: Number of species including boundary species.
      source
      Edge and node data
      VoronoiFVM.Node — Type
      mutable struct Node{Tc, Tp, Ti} <: VoronoiFVM.AbstractNode{Tc, Tp, Ti}
      Structure holding local node information.
      • index::Any: Index in grid
      • region::Any: Inner region number
      • nspec::Any: Number of species defined in node
      • icell::Any: Number of discretization cell the node is invoked from
      • coord::Matrix: Grid coordinates
      • cellnodes::Matrix: Grid cell nodes
      • cellregions::Vector: Grid cell regions
      • time::Float64: System time
      • embedparam::Float64: Current value of embedding parameter
      • params::Vector: parameters
      • fac::Float64: Form factor
      • _idx::Any: Local loop index
      source
      VoronoiFVM.BNode — Type
      mutable struct BNode{Tv, Tc, Tp, Ti} <: VoronoiFVM.AbstractNode{Tc, Tp, Ti}
      Structure holding local boundary  node information.
      • index::Any: Index in grid
      • ibface::Any: BFace number it is called from
      • ibnode::Any: local node number
      • region::Any: Boundary region number
      • cellregions::Vector
      • nspec::Any: Number of species defined in node
      • coord::Matrix: Grid coordinates
      • bfacenodes::Matrix
      • bfaceregions::Vector
      • allcellregions::Vector
      • bfacecells::Adjacency
      • Dirichlet::Any
      • time::Float64: System time
      • embedparam::Float64: Current value of embedding parameter
      • params::Vector
      • dirichlet_value::Vector
      • fac::Float64
      source
      VoronoiFVM.Edge — Type
      mutable struct Edge{Tc, Tp, Ti} <: VoronoiFVM.AbstractEdge{Tc, Tp, Ti}
      Structure holding local edge information.
      • index::Any: Index in grid
      • node::Vector: Index
      • region::Any: Inner region number corresponding to edge
      • nspec::Any: Number of species defined in edge
      • icell::Any: Number of discretization cell the edge is invoked from
      • coord::Matrix: Grid coordinates
      • cellx::Matrix
      • edgenodes::Matrix
      • cellregions::Vector
      • has_celledges::Bool
      • time::Float64: System time
      • embedparam::Float64: Current value of embedding parameter
      • params::Vector
      • fac::Float64: Form factor
      • _idx::Any: Local loop index
      • outflownoderegions::Union{Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}}
      • outflownode::Int64: Outflow node
      source
      VoronoiFVM.BEdge — Type
      mutable struct BEdge{Tc, Tp, Ti} <: VoronoiFVM.AbstractEdge{Tc, Tp, Ti}
      Structure holding local edge information.
      • index::Any: Index in grid
      • node::Vector: Index
      • region::Any: Inner region number corresponding to edge
      • nspec::Any: Number of species defined in edge
      • icell::Any: Number of discretization cell the edge is invoked from
      • coord::Matrix: Grid coordinates
      • bedgenodes::Matrix
      • bfaceedges::Matrix
      • bfaceregions::Vector
      • time::Float64: System time
      • embedparam::Float64: Current value of embedding parameter
      • params::Vector
      • fac::Float64
      source
      Special functions
      VoronoiFVM.fbernoulli — Function
      fbernoulli(x)
-
      Bernoulli function $B(x)=\frac{x}{e^x-1}$ for exponentially fitted upwinding.
      The name fbernoulli has been chosen to avoid confusion with Bernoulli from JuliaStats/Distributions.jl
      Returns a real number containing the result.
      source
      VoronoiFVM.fbernoulli_pm — Function
      fbernoulli_pm(x)
-
      Bernoulli function $B(x)=\frac{x}{e^x-1}$ for exponentially fitted upwind, joint evaluation for positive and negative argument
      Usually, we need $B(x), B(-x)$ together,  and it is cheaper to calculate them together.
      Returns two real numbers containing the result for argument x and argument -x.
      The error in comparison with the evaluation of the original expression with BigFloat is less than 1.0e-15
      source
      VoronoiFVM.inplace_linsolve! — Method
      inplace_linsolve!(A, b)
-
      Non-allocating, non-pivoting inplace solution of square linear system of equations A*x=b using Doolittle's method.
      After solution, A will contain the LU factorization, and b the result.
      A pivoting version is available with Julia v1.9.
      source
      VoronoiFVM.inplace_linsolve! — Method
      inplace_linsolve!(A, b, ipiv)
-
      Non-allocating, pivoting, inplace solution of square linear system of equations A*x=b using LU factorization from RecursiveFactorizations.jl.  
      After solution, A will contain the LU factorization, and b the result. ipiv must be an Int64 vector of the same length as b.
      Info
      Needs Julia v1.9 or later
      source
      
+    )

      Constructor for physics data. For the meaning of the optional keyword arguments, see VoronoiFVM.System(grid::ExtendableGrid; kwargs...).

      source

      Edge and node data

      VoronoiFVM.Node — Type
      mutable struct Node{Tc, Tp, Ti} <: VoronoiFVM.AbstractNode{Tc, Tp, Ti}

      Structure holding local node information.

      • index::Any: Index in grid
      • region::Any: Inner region number
      • nspec::Any: Number of species defined in node
      • icell::Any: Number of discretization cell the node is invoked from
      • coord::Matrix: Grid coordinates
      • cellnodes::Matrix: Grid cell nodes
      • cellregions::Vector: Grid cell regions
      • time::Float64: System time
      • embedparam::Float64: Current value of embedding parameter
      • params::Vector: parameters
      • fac::Float64: Form factor
      • _idx::Any: Local loop index
      source
      VoronoiFVM.BNode — Type
      mutable struct BNode{Tv, Tc, Tp, Ti} <: VoronoiFVM.AbstractNode{Tc, Tp, Ti}

      Structure holding local boundary node information.

      • index::Any: Index in grid
      • ibface::Any: BFace number it is called from
      • ibnode::Any: local node number
      • region::Any: Boundary region number

      • cellregions::Vector

      • nspec::Any: Number of species defined in node

      • coord::Matrix: Grid coordinates

      • bfacenodes::Matrix

      • bfaceregions::Vector

      • allcellregions::Vector

      • bfacecells::Adjacency

      • Dirichlet::Any

      • time::Float64: System time

      • embedparam::Float64: Current value of embedding parameter

      • params::Vector

      • dirichlet_value::Vector

      • fac::Float64

      source
      VoronoiFVM.Edge — Type
      mutable struct Edge{Tc, Tp, Ti} <: VoronoiFVM.AbstractEdge{Tc, Tp, Ti}

      Structure holding local edge information.

      • index::Any: Index in grid
      • node::Vector: Index
      • region::Any: Inner region number corresponding to edge
      • nspec::Any: Number of species defined in edge
      • icell::Any: Number of discretization cell the edge is invoked from
      • coord::Matrix: Grid coordinates

      • cellx::Matrix

      • edgenodes::Matrix

      • cellregions::Vector

      • has_celledges::Bool

      • time::Float64: System time

      • embedparam::Float64: Current value of embedding parameter

      • params::Vector

      • fac::Float64: Form factor

      • _idx::Any: Local loop index

      • outflownoderegions::Union{Nothing, SparseArrays.SparseMatrixCSC{Bool, Int64}}

      • outflownode::Int64: Outflow node

      source
      VoronoiFVM.BEdge — Type
      mutable struct BEdge{Tc, Tp, Ti} <: VoronoiFVM.AbstractEdge{Tc, Tp, Ti}

      Structure holding local edge information.

      • index::Any: Index in grid
      • node::Vector: Index
      • region::Any: Inner region number corresponding to edge
      • nspec::Any: Number of species defined in edge
      • icell::Any: Number of discretization cell the edge is invoked from
      • coord::Matrix: Grid coordinates

      • bedgenodes::Matrix

      • bfaceedges::Matrix

      • bfaceregions::Vector

      • time::Float64: System time

      • embedparam::Float64: Current value of embedding parameter

      • params::Vector

      • fac::Float64

      source

      Special functions

      VoronoiFVM.fbernoulli — Function
      fbernoulli(x)
+

      Bernoulli function $B(x)=\frac{x}{e^x-1}$ for exponentially fitted upwinding.

      The name fbernoulli has been chosen to avoid confusion with Bernoulli from JuliaStats/Distributions.jl

      Returns a real number containing the result.

      source
      VoronoiFVM.fbernoulli_pm — Function
      fbernoulli_pm(x)
+

      Bernoulli function $B(x)=\frac{x}{e^x-1}$ for exponentially fitted upwind, joint evaluation for positive and negative argument

      Usually, we need $B(x), B(-x)$ together, and it is cheaper to calculate them together.

      Returns two real numbers containing the result for argument x and argument -x.

      The error in comparison with the evaluation of the original expression with BigFloat is less than 1.0e-15

      source
      VoronoiFVM.inplace_linsolve! — Method
      inplace_linsolve!(A, b)
+

      Non-allocating, non-pivoting inplace solution of square linear system of equations A*x=b using Doolittle's method.

      After solution, A will contain the LU factorization, and b the result.

      A pivoting version is available with Julia v1.9.

      source
      VoronoiFVM.inplace_linsolve! — Method
      inplace_linsolve!(A, b, ipiv)
+

      Non-allocating, pivoting, inplace solution of square linear system of equations A*x=b using LU factorization from RecursiveFactorizations.jl.

      After solution, A will contain the LU factorization, and b the result. ipiv must be an Int64 vector of the same length as b.

      Info

      Needs Julia v1.9 or later

      source
      diff --git a/dev/post/index.html b/dev/post/index.html index 65de0897c..5df56d1b2 100644 --- a/dev/post/index.html +++ b/dev/post/index.html @@ -1,11 +1,11 @@ -Postprocessing · VoronoiFVM.jl
      Edit on GitHub

      Postprocessing

      Plotting

      Plotting can be performed using the package GridVisualize.jl. This package extends the API with a couple of methods:

      GridVisualize.gridplot! — Function
      gridplot!(
+Postprocessing · VoronoiFVM.jl
      Postprocessing
      Plotting
      Plotting can be performed using the package GridVisualize.jl. This package extends the API with a couple of methods:
      GridVisualize.scalarplot — Function
      scalarplot(
     sys::VoronoiFVM.AbstractSystem,
     sol::AbstractMatrix;
     species,
@@ -20,7 +20,7 @@
     tscale,
     kwargs...
 ) -> Any
-
      Plot one species from transient solution
      source
      GridVisualize.scalarplot! — Function
      scalarplot!(
     vis,
     sys::VoronoiFVM.AbstractSystem,
     sol::AbstractMatrix;
@@ -38,51 +38,51 @@
     tlabel,
     kwargs...
 ) -> Any
-
      Plot one species from transient solution
      source
      Norms & volumes
      Norms & volumes
      LinearAlgebra.norm — Function
      norm(system, u)
 norm(system, u, p)
-
      Calculate Euklidean norm of the degree of freedom vector.
      source
      VoronoiFVM.lpnorm — Function
      lpnorm(sys, u, p)
 lpnorm(sys, u, p, species_weights)
-
      Calculate weighted discrete $L^p$ norm of a solution vector.
      source
      VoronoiFVM.l2norm — Function
      l2norm(sys, u)
 l2norm(sys, u, species_weights)
-
      Calculate weigthed discrete $L^2(\Omega)$ norm of a solution vector. 
      source
      VoronoiFVM.w1pseminorm — Function
      w1pseminorm(sys, u, p)
 w1pseminorm(sys, u, p, species_weights)
-
      Calculate weighted discrete $W^{1,p}(\Omega)$ seminorm of a solution vector.
      source
      VoronoiFVM.h1seminorm — Function
      h1seminorm(sys, u)
+
      Calculate weighted discrete $W^{1,p}(\Omega)$ seminorm of a solution vector.
      source
      VoronoiFVM.h1seminorm — Function
      h1seminorm(sys, u)
 h1seminorm(sys, u, species_weights)
-
      Calculate weighted discrete $H^1(\Omega)$ seminorm of a solution vector.
      source
      VoronoiFVM.w1pnorm — Function
      w1pnorm(sys, u, p)
+
      Calculate weighted discrete $H^1(\Omega)$ seminorm of a solution vector.
      source
      VoronoiFVM.w1pnorm — Function
      w1pnorm(sys, u, p)
 w1pnorm(sys, u, p, species_weights)
-
      Calculate weighted discrete $W^{1,p}(\Omega)$ norm of a solution vector.
      source
      VoronoiFVM.h1norm — Function
      h1norm(sys, u)
+
      Calculate weighted discrete $W^{1,p}(\Omega)$ norm of a solution vector.
      source
      VoronoiFVM.h1norm — Function
      h1norm(sys, u)
 h1norm(sys, u, species_weights)
-
      Calculate weighted discrete $H^1(\Omega)$ norm of a solution vector.
      source
      VoronoiFVM.lpw1pseminorm — Function
      lpw1pseminorm(sys, u, p)
 lpw1pseminorm(sys, u, p, species_weights)
-
      Calculate weighted discrete $L^p([0,T];W^{1,p}(\Omega))$ seminorm of a transient solution.
      source
      VoronoiFVM.l2h1seminorm — Function
      l2h1seminorm(sys, u)
+
      Calculate weighted discrete $L^p([0,T];W^{1,p}(\Omega))$ seminorm of a transient solution.
      source
      VoronoiFVM.l2h1seminorm — Function
      l2h1seminorm(sys, u)
 l2h1seminorm(sys, u, species_weights)
-
      Calculate weighted discrete $L^2([0,T];H^1(\Omega))$ seminorm of a transient solution.
      source
      VoronoiFVM.lpw1pnorm — Function
      lpw1pnorm(sys, u, p)
+
      Calculate weighted discrete $L^2([0,T];H^1(\Omega))$ seminorm of a transient solution.
      source
      VoronoiFVM.lpw1pnorm — Function
      lpw1pnorm(sys, u, p)
 lpw1pnorm(sys, u, p, species_weights)
-
      Calculate weighted discrete $L^p([0,T];W^{1,p}(\Omega))$ norm of a transient solution.
      source
      VoronoiFVM.l2h1norm — Function
      l2h1norm(sys, u)
+
      Calculate weighted discrete $L^p([0,T];W^{1,p}(\Omega))$ norm of a transient solution.
      source
      VoronoiFVM.l2h1norm — Function
      l2h1norm(sys, u)
 l2h1norm(sys, u, species_weights)
-
      Calculate weighted discrete $L^2([0,T];H^1(\Omega))$ norm of a transient solution.
      source
      Solution integrals
      VoronoiFVM.integrate — Method
      integrate(system,F,U; boundary=false)
      Integrate node function (same signature as reaction or storage)  F of  solution vector region-wise over domain or boundary. The result is an nspec x nregion vector.
      source
      VoronoiFVM.edgeintegrate — Function
      edgeintegrate(system,F,U; boundary=false)
      Integrate edge function (same signature as flux function)  F of  solution vector region-wise over domain or boundary. The result is an nspec x nregion vector.
      source
      Nodal flux reconstruction
      VoronoiFVM.nodeflux — Function
      nodeflux(system, U)
+
      Calculate weighted discrete $L^2([0,T];H^1(\Omega))$ norm of a transient solution.
      source
      Solution integrals
      VoronoiFVM.integrate — Method
      integrate(system,F,U; boundary=false)
      Integrate node function (same signature as reaction or storage)  F of  solution vector region-wise over domain or boundary. The result is an nspec x nregion vector.
      source
      VoronoiFVM.edgeintegrate — Function
      edgeintegrate(system,F,U; boundary=false)
      Integrate edge function (same signature as flux function)  F of  solution vector region-wise over domain or boundary. The result is an nspec x nregion vector.
      source
      Nodal flux reconstruction
      VoronoiFVM.nodeflux — Function
      nodeflux(system, U)
 
      Reconstruction of  edge flux as  vector function  on the nodes  of the triangulation.  The result  can be seen as a  piecewiesw linear vector function in the FEM space spanned by the discretization nodes exhibiting the flux density.  
      The reconstruction is based on the  "magic formula" R. Eymard, T. Gallouet, R. Herbin, IMA Journal of Numerical Analysis (2006) 26, 326−353, Lemma 2.4 .
      The return value is a dim x nspec x nnodes vector. The flux of species i can  e.g. plotted via GridVisualize.vectorplot.
      Example:
          ispec=3
     vis=GridVisualizer(Plotter=Plotter)
     scalarplot!(vis,grid,solution[ispec,:],clear=true,colormap=:summer)
     vectorplot!(vis,grid,nf[:,ispec,:],clear=false)
-    reveal(vis)
      CAVEAT: there is a possible unsolved problem with the values at domain  corners in the code. Please see any potential boundary artifacts as a manifestation of this issue and report them.
      source
      Boundary flux calculation
      VoronoiFVM.TestFunctionFactory — Type
      mutable struct TestFunctionFactory
      Data structure containing DenseSystem used to calculate test functions for boundary flux calculations.
      • system::VoronoiFVM.AbstractSystem: Original system
      • tfsystem::VoronoiFVM.System{Tv, Tc, Ti, Tm, Matrix{Ti}, Matrix{Tv}} where {Tv, Tc, Ti, Tm}: Test function system
      • control::SolverControl: Solver control
      source
      VoronoiFVM.TestFunctionFactory — Method
      TestFunctionFactory(
+    reveal(vis)
      CAVEAT: there is a possible unsolved problem with the values at domain  corners in the code. Please see any potential boundary artifacts as a manifestation of this issue and report them.
      source
      Boundary flux calculation
      VoronoiFVM.TestFunctionFactory — Type
      mutable struct TestFunctionFactory
      Data structure containing DenseSystem used to calculate test functions for boundary flux calculations.
      • system::VoronoiFVM.AbstractSystem: Original system
      • tfsystem::VoronoiFVM.System{Tv, Tc, Ti, Tm, Matrix{Ti}, Matrix{Tv}} where {Tv, Tc, Ti, Tm}: Test function system
      • control::SolverControl: Solver control
      source
      VoronoiFVM.TestFunctionFactory — Method
      TestFunctionFactory(
     system::VoronoiFVM.AbstractSystem;
     control
 ) -> TestFunctionFactory
-
      Constructor for TestFunctionFactory from System
      source
      VoronoiFVM.integrate — Method
      integrate(system, tf, U; kwargs...)
-
      Calculate test function integral for steady state solution.
      source
      VoronoiFVM.integrate — Method
      integrate(system, tf, U, Uold, tstep; params)
-
      Calculate test function integral for transient solution.
      source
      VoronoiFVM.testfunction — Method
      testfunction(factory::TestFunctionFactory, bc0, bc1) -> Any
-
      Create testfunction which has Dirichlet zero boundary conditions  for boundary regions in bc0 and Dirichlet one boundary conditions  for boundary regions in bc1.
      source
      Impedance calculatiom
      Impedance calculation can be seen as a postprocessing step after the solution of the unexcited stationary system.
      VoronoiFVM.ImpedanceSystem — Type
      mutable struct ImpedanceSystem{Tv} <: VoronoiFVM.AbstractImpedanceSystem{Tv}
      Concrete type for impedance system.
      • sysnzval::AbstractArray{Complex{Tv}, 1} where Tv: Nonzero pattern of time domain system matrix
      • storderiv::AbstractMatrix: Derivative of storage term
      • matrix::AbstractArray{Complex{Tv}, 2} where Tv: Complex matrix of impedance system
      • F::AbstractArray{Complex{Tv}, 2} where Tv: Right hand side of impedance system
      • U0::AbstractMatrix: Stationary state
      source
      VoronoiFVM.ImpedanceSystem — Method
      ImpedanceSystem(system, U0, excited_spec, excited_bc)
-
      Construct impedance system from time domain system sys and steady state solution U0 under the assumption of a periodic perturbation of species excited_spec at  boundary excited_bc.
      source
      VoronoiFVM.ImpedanceSystem — Method
      ImpedanceSystem(system, U0; λ0)
-
      Construct impedance system from time domain system sys and steady state solution U0
      source
      VoronoiFVM.integrate — Method
      integrate(system, tf, U; kwargs...)
+
      Calculate test function integral for steady state solution.
      source
      VoronoiFVM.integrate — Method
      integrate(system, tf, U, Uold, tstep; params)
+
      Calculate test function integral for transient solution.
      source
      VoronoiFVM.testfunction — Method
      testfunction(factory::TestFunctionFactory, bc0, bc1) -> Any
+
      Create testfunction which has Dirichlet zero boundary conditions  for boundary regions in bc0 and Dirichlet one boundary conditions  for boundary regions in bc1.
      source
      Impedance calculatiom
      Impedance calculation can be seen as a postprocessing step after the solution of the unexcited stationary system.
      VoronoiFVM.ImpedanceSystem — Type
      mutable struct ImpedanceSystem{Tv} <: VoronoiFVM.AbstractImpedanceSystem{Tv}
      Concrete type for impedance system.
      • sysnzval::AbstractArray{Complex{Tv}, 1} where Tv: Nonzero pattern of time domain system matrix
      • storderiv::AbstractMatrix: Derivative of storage term
      • matrix::AbstractArray{Complex{Tv}, 2} where Tv: Complex matrix of impedance system
      • F::AbstractArray{Complex{Tv}, 2} where Tv: Right hand side of impedance system
      • U0::AbstractMatrix: Stationary state
      source
      VoronoiFVM.ImpedanceSystem — Method
      ImpedanceSystem(system, U0, excited_spec, excited_bc)
+
      Construct impedance system from time domain system sys and steady state solution U0 under the assumption of a periodic perturbation of species excited_spec at  boundary excited_bc.
      source
      VoronoiFVM.ImpedanceSystem — Method
      ImpedanceSystem(system, U0; λ0)
+
      Construct impedance system from time domain system sys and steady state solution U0
      source
      VoronoiFVM.impedance — Method
      impedance(impedance_system,ω, U0 ,
           excited_spec, excited_bc, excited_bcval,
            dmeas_stdy,
            dmeas_tran 
            )
-    
      Calculate impedance.
      • ω:  frequency 
      • U0: steady state slution
      • dmeas_stdy: Derivative of steady state part of measurement functional
      • dmeas_tran  Derivative of transient part of the measurement functional
      source
      VoronoiFVM.measurement_derivative — Method
      measurement_derivative(system, measurement_functional, U0)
-
      Calculate the derivative of the scalar measurement functional at steady state U0
      Usually, this functional is  a test function integral.  Initially, we assume that its value depends on all unknowns of the system.
      source
      
+

      Calculate impedance.

      • ω: frequency
      • U0: steady state slution
      • dmeas_stdy: Derivative of steady state part of measurement functional
      • dmeas_tran Derivative of transient part of the measurement functional
      source
      VoronoiFVM.measurement_derivative — Method
      measurement_derivative(system, measurement_functional, U0)
+

      Calculate the derivative of the scalar measurement functional at steady state U0

      Usually, this functional is a test function integral. Initially, we assume that its value depends on all unknowns of the system.

      source
      diff --git a/dev/quantities/index.html b/dev/quantities/index.html index 7639ffa43..db9eeca60 100644 --- a/dev/quantities/index.html +++ b/dev/quantities/index.html @@ -1,4 +1,4 @@ -Quantities · VoronoiFVM.jl
      Edit on GitHub

      Quantities

      The concept of quantities is implemented on top of the concept of species numbers. They have been introduces in order to be able to handle discontinuities at interfaces.

      VoronoiFVM.ContinuousQuantity — Type
      struct ContinuousQuantity{Ti} <: VoronoiFVM.AbstractQuantity{Ti}

      A continuous quantity is represented by exactly one species number

      • ispec::Any: Species number representing the quantity
      • id::Any: Quantity identifier allowing to use the quantity as index in parameter fields
      source
      VoronoiFVM.ContinuousQuantity — Method
       ContinuousQuantity(system,regions; ispec=0, id=0)

      Add continuous quantity to the regions listed in regions.

      Unless specified in ispec, the species number is generated automatically.

      Unless specified by id, the quantity ID is generated automatically.

      source
      VoronoiFVM.DiscontinuousQuantity — Type
      struct DiscontinuousQuantity{Ti} <: VoronoiFVM.AbstractQuantity{Ti}

      A discontinuous quantity is represented by different species in neighboring regions.

      • regionspec::Vector: Species numbers representing the quantity in each region
      • id::Any: Quantity identifier allowing to use the quantity as index in parameter fields
      source
      VoronoiFVM.DiscontinuousQuantity — Method
       DiscontinuousQuantity(system,regions; regionspec=nothing, id=0)

      Add discontinuous quantity to the regions listed in regions.

      Unless specified in regionspec, the species numbers for each region are generated automatically.

      Unless specified by id, the quantity ID is generated automatically.

      source
      VoronoiFVM.InterfaceQuantity — Type
      struct InterfaceQuantity{Ti} <: VoronoiFVM.AbstractQuantity{Ti}

      An interface quantity is represented by exactly one species number

      • ispec::Any: Species number representing the quantity
      • bregspec::Vector: boundary regions, where interface quantity is defined
      • id::Any: Quantity identifier allowing to use the quantity as index in parameter fields
      source
      VoronoiFVM.InterfaceQuantity — Method
       InterfaceQuantity(system,regions; ispec=0, id=0)

      Add interface quantity to the boundary regions given in breg.

      Unless specified in ispec, the species number is generated automatically.

      Unless specified by id, the quantity ID is generated automatically.

      source
      Base.getindex — Method
      A[q]

      Access columns of vectors A using id of quantity q. This is meant for vectors indexed by species.

      source
      Base.getindex — Method
      M[q,i]

      Access columns M using id of quantity q. This is meant for nspecies x nregions matrices e.g. defining parameters.

      source
      Base.getindex — Method
      bnode[quantity,ireg]

      Return species number of discontinuous quantity region ireg adjacent to BNode.

      source
      Base.getindex — Method
      bnode[quantity]

      Return species number of discontinuous quantity region ireg adjacent to BNode for outer boundary nodes.

      source
      Base.getindex — Method
      u[q,j]

      Return value of quantity in unknowns on edge in flux callbacks.

      source
      Base.getindex — Method
      u[q]

      Return value of quantity in unknowns on node in node callbacks.

      source
      Base.getindex — Method
      u[q,ireg]

      Return value of discontinuous quantity in unknowns adjacent to unknowns on boundary node.

      source
      Base.setindex! — Method
      A[q]

      Set element of A using id of quantity q This is meant for vectors indexed by species.

      source
      Base.setindex! — Method
      M[q,i]

      Set element of M using id of quantity q. This is meant for nspecies x nregions matrices e.g. defining parameters.

      source
      Base.setindex! — Method
      f[q,ireg]=v

      Set rhs value for discontinuous quantity in adjacent regions of boundary node.

      source
      VoronoiFVM.subgrids — Method
      subgrids(quantity, system)

      Return a vector of subgrids containing a subgrid for each region where discontinuous quantity is defined.

      source
      VoronoiFVM.views — Method
      views(quantity, subgrids,system)

      Return a vector of solutions containing the solutions with respect tp each region where discontinuous quantity is defined.

      source
      +Quantities · VoronoiFVM.jl

      Quantities

      The concept of quantities is implemented on top of the concept of species numbers. They have been introduces in order to be able to handle discontinuities at interfaces.

      VoronoiFVM.ContinuousQuantity — Type
      struct ContinuousQuantity{Ti} <: VoronoiFVM.AbstractQuantity{Ti}

      A continuous quantity is represented by exactly one species number

      • ispec::Any: Species number representing the quantity
      • id::Any: Quantity identifier allowing to use the quantity as index in parameter fields
      source
      VoronoiFVM.ContinuousQuantity — Method
       ContinuousQuantity(system,regions; ispec=0, id=0)

      Add continuous quantity to the regions listed in regions.

      Unless specified in ispec, the species number is generated automatically.

      Unless specified by id, the quantity ID is generated automatically.

      source
      VoronoiFVM.DiscontinuousQuantity — Type
      struct DiscontinuousQuantity{Ti} <: VoronoiFVM.AbstractQuantity{Ti}

      A discontinuous quantity is represented by different species in neighboring regions.

      • regionspec::Vector: Species numbers representing the quantity in each region
      • id::Any: Quantity identifier allowing to use the quantity as index in parameter fields
      source
      VoronoiFVM.DiscontinuousQuantity — Method
       DiscontinuousQuantity(system,regions; regionspec=nothing, id=0)

      Add discontinuous quantity to the regions listed in regions.

      Unless specified in regionspec, the species numbers for each region are generated automatically.

      Unless specified by id, the quantity ID is generated automatically.

      source
      VoronoiFVM.InterfaceQuantity — Type
      struct InterfaceQuantity{Ti} <: VoronoiFVM.AbstractQuantity{Ti}

      An interface quantity is represented by exactly one species number

      • ispec::Any: Species number representing the quantity
      • bregspec::Vector: boundary regions, where interface quantity is defined
      • id::Any: Quantity identifier allowing to use the quantity as index in parameter fields
      source
      VoronoiFVM.InterfaceQuantity — Method
       InterfaceQuantity(system,regions; ispec=0, id=0)

      Add interface quantity to the boundary regions given in breg.

      Unless specified in ispec, the species number is generated automatically.

      Unless specified by id, the quantity ID is generated automatically.

      source
      Base.getindex — Method
      A[q]

      Access columns of vectors A using id of quantity q. This is meant for vectors indexed by species.

      source
      Base.getindex — Method
      M[q,i]

      Access columns M using id of quantity q. This is meant for nspecies x nregions matrices e.g. defining parameters.

      source
      Base.getindex — Method
      bnode[quantity,ireg]

      Return species number of discontinuous quantity region ireg adjacent to BNode.

      source
      Base.getindex — Method
      bnode[quantity]

      Return species number of discontinuous quantity region ireg adjacent to BNode for outer boundary nodes.

      source
      Base.getindex — Method
      u[q,j]

      Return value of quantity in unknowns on edge in flux callbacks.

      source
      Base.getindex — Method
      u[q]

      Return value of quantity in unknowns on node in node callbacks.

      source
      Base.getindex — Method
      u[q,ireg]

      Return value of discontinuous quantity in unknowns adjacent to unknowns on boundary node.

      source
      Base.setindex! — Method
      A[q]

      Set element of A using id of quantity q This is meant for vectors indexed by species.

      source
      Base.setindex! — Method
      M[q,i]

      Set element of M using id of quantity q. This is meant for nspecies x nregions matrices e.g. defining parameters.

      source
      Base.setindex! — Method
      f[q,ireg]=v

      Set rhs value for discontinuous quantity in adjacent regions of boundary node.

      source
      VoronoiFVM.subgrids — Method
      subgrids(quantity, system)

      Return a vector of subgrids containing a subgrid for each region where discontinuous quantity is defined.

      source
      VoronoiFVM.views — Method
      views(quantity, subgrids,system)

      Return a vector of solutions containing the solutions with respect tp each region where discontinuous quantity is defined.

      source
      diff --git a/dev/runexamples/index.html b/dev/runexamples/index.html index afb2d83d2..e5f26c1e4 100644 --- a/dev/runexamples/index.html +++ b/dev/runexamples/index.html @@ -1,5 +1,5 @@ -About the examples · VoronoiFVM.jl
      Edit on GitHub

      About the examples

      The examples have been designed with the following issues in mind:

      • they run from the Julia REPL
      • each example is a Julia module named similar to the basename of the example file.
      • an example can be used as the starting point for a project
      • the examples at the same time comprise the test suite for VoronoiFVM.

      Since the creation of these examples, the API has been updated and simplified.

      Running the examples

      Plotting is performed using the GridVisualize.jl package which interfaces PyPlot.jl, Plots.jl, Makie.jl.

      In order to run ExampleXXX, perform the following steps:

      • Download the example file (e.g. via the source code link at the top)
      • Call Julia with an Julia environment which contains VoronoiFVM.jl, ExtendableGrids.jl, GridVisualize.jl and e.g. PyPlot.jl
      • include("ExampleXXX.jl")
      • Run the example via ExampleXXX.main(Plotter=PyPlot)

      Due to the encapsulation into modules, you can load as many examples as you like.

      If you want to modify the example, consider using Revise.jl and includet.

      Performance with closures

      VoronoiFVM provides two flavors of calbacks for constitutive functions:

      • Callbacks with data parameoter. data is declared as part of Physics and passed down to the callbacks
      • Callbacks without data parameter. Here, the parameters of the physics callbacks are accessed via closures, i.e. from within the scope of the definition of the particular function.

      While the second method is very convenient to use, it comes with a serious performance pitfall: if a variable in the closure is assigned twice, Julia becomes unsure about it's type and therefore "boxes" it, i.e. it creates a wrapper struct around the variable value which is able to track its potentially changing type. The serious consequence of this is that assignments to a boxed variable lead to allocations, which are a serious performance hit if they occur in loops over grid nodes or edges.

      This behaviour is explained in the Julia documentation.

      Here is an example which comes close to the situation in VoronoiFVM:

      function ttype_boxed(n)
+About the examples · VoronoiFVM.jl
      About the examples
      The examples have been designed with the following issues in mind:
      • they run from the Julia REPL
      • each example is a Julia module named similar to the basename of the example file.
      • an example can be used as the starting point for a project 
      • the examples at the same time comprise the test suite for VoronoiFVM.
      Since the creation of these examples, the API has been updated and simplified.
      Running the examples
      Plotting is performed using the GridVisualize.jl package which interfaces PyPlot.jl, Plots.jl, Makie.jl.
      In order to run ExampleXXX, perform the following steps:
      • Download the example file (e.g. via the source code link at the top)
      • Call Julia with  an Julia environment which contains VoronoiFVM.jl, ExtendableGrids.jl, GridVisualize.jl  and e.g. PyPlot.jl
      • include("ExampleXXX.jl")
      • Run the example via ExampleXXX.main(Plotter=PyPlot)
      Due to the encapsulation into modules, you can load as many examples as you like.
      If you want to modify the example, consider using Revise.jl and includet. 
      Performance with  closures
      VoronoiFVM provides two flavors of calbacks for constitutive functions: 
      • Callbacks with data parameoter. data is declared as part of Physics and passed down to the callbacks
      • Callbacks without data parameter. Here, the parameters of the  physics callbacks are accessed via closures, i.e. from within the  scope of the definition of the particular function.
      While the  second method is  very convenient to  use, it comes  with a serious performance pitfall: if a  variable in the closure is assigned twice, Julia becomes unsure about  it's type and therefore "boxes" it, i.e. it  creates a wrapper struct  around the variable value  which is able to track  its potentially changing type.  The serious consequence of this is that assignments to a boxed variable lead to allocations, which are a serious performance hit if they occur in loops over grid nodes or edges.
      This behaviour is explained in the Julia documentation.
      Here is an example which comes close to the situation in VoronoiFVM:
      function ttype_boxed(n)
     u=rand(n)
     v=similar(u)
     a=2.0
@@ -15,4 +15,4 @@
     dostuff(u)=a*u
     @allocated map!(dostuff,v,u)
 end
-ttype_annotated(10)
      0
      
+ttype_annotated(10)
      0
      diff --git a/dev/search/index.html b/dev/search/index.html deleted file mode 100644 index d581345d2..000000000 --- a/dev/search/index.html +++ /dev/null @@ -1,2 +0,0 @@ - -Search · VoronoiFVM.jl

      Loading search...

        diff --git a/dev/solutions/index.html b/dev/solutions/index.html index 3c45bf2bd..64ed670e6 100644 --- a/dev/solutions/index.html +++ b/dev/solutions/index.html @@ -1,20 +1,20 @@ -Solution objects · VoronoiFVM.jl
        Edit on GitHub

        Solution objects

        Dense solution arrays

        VoronoiFVM._add — Method
        _add(U::Array{Tv, 2}, idof, val) -> Any
-

        Add residual value into global degree of freedom

        source

        Sparse solution arrays

        VoronoiFVM.SparseSolutionArray — Type
        struct SparseSolutionArray{Tv, Ti} <: AbstractArray{Tv, 2}

        Struct holding solution information for SparseSystem. Solution is stored in a sparse matrix structure.

        This class plays well with the abstract array interface.

        Fields:

        • node_dof::SparseArrays.SparseMatrixCSC{Tv, Ti} where {Tv, Ti}: Sparse matrix holding actual data.
        source
        Base.copy — Method
        copy(this)
-

        Create a copy of sparse solution array

        source
        Base.similar — Method
        similar(this)
-

        Create a similar uninitialized sparse solution array

        source
        VoronoiFVM._add — Method
        _add(U::VoronoiFVM.SparseSolutionArray, idof, val) -> Any
-

        Add residual value into global degree of freedom

        source
        VoronoiFVM.dof — Method
        dof(a, i, j)
-

        Get number of degree of freedom. Return 0 if species is not defined in node.

        source

        Transient solution

        VoronoiFVM.TransientSolution — Type
        mutable struct TransientSolution{T, N, A, B} <: VoronoiFVM.AbstractTransientSolution{T, N, A, B}

        Transient solution structure

        Fields

        • u::Any: Vector of solutions
        • t::Any: Vector of times

        Interface

        Object of this type adhere to the AbstractDiffEqArray interface. For indexing and interpolation, see https://diffeq.sciml.ai/stable/basics/solution/.

        In particular, a TransientSolution sol can be accessed as follows:

        • sol[i] contains the solution for timestep i
        • sol[ispec,:,i] contains the solution for component ispec at timestep i
        • sol(t) returns a (linearly) interpolated solution value for t.
        • sol.t[i] is the corresponding time for timestep i
        • sol[ispec,ix,i] refers to solution of component ispec at node ix at moment i
        source
        VoronoiFVM.TransientSolution — Method
        TransientSolution(t0,inival;
+Solution objects · VoronoiFVM.jl
        Solution objects
        Dense solution arrays
        VoronoiFVM._add — Method
        _add(U::Array{Tv, 2}, idof, val) -> Any
+
        Add residual value into global degree of freedom
        source
        Sparse solution arrays
        VoronoiFVM.SparseSolutionArray — Type
        struct SparseSolutionArray{Tv, Ti} <: AbstractArray{Tv, 2}
        Struct holding solution information for SparseSystem. Solution is stored in a sparse matrix structure.
        This class plays well with the abstract array interface.
        Fields:
        • node_dof::SparseArrays.SparseMatrixCSC{Tv, Ti} where {Tv, Ti}: Sparse matrix holding actual data.
        source
        Base.copy — Method
        copy(this)
+
        Create a copy of sparse solution array
        source
        Base.similar — Method
        similar(this)
+
        Create a similar uninitialized sparse solution array
        source
        VoronoiFVM._add — Method
        _add(U::VoronoiFVM.SparseSolutionArray, idof, val) -> Any
+
        Add residual value into global degree of freedom
        source
        VoronoiFVM.dof — Method
        dof(a, i, j)
+
        Get number of degree of freedom. Return 0 if species is not defined in node.
        source
        Transient solution
        VoronoiFVM.TransientSolution — Type
        mutable struct TransientSolution{T, N, A, B} <: VoronoiFVM.AbstractTransientSolution{T, N, A, B}
        Transient solution structure
        Fields
        • u::Any: Vector of solutions
        • t::Any: Vector of times
        Interface
        Object of this type adhere to the AbstractDiffEqArray  interface. For indexing and interpolation, see https://diffeq.sciml.ai/stable/basics/solution/.
        In particular, a TransientSolution sol can be accessed as follows:
        • sol[i] contains the solution for timestep i
        • sol[ispec,:,i] contains the solution for component ispec at timestep i
        • sol(t) returns a (linearly) interpolated solution value for t.
        • sol.t[i] is the corresponding time for timestep i
        • sol[ispec,ix,i] refers to solution of component ispec at node ix at moment i
        source
        VoronoiFVM.TransientSolution — Method
        TransientSolution(t0,inival;
                   in_memory=true,
                   keep_open=true,
-                  fname=tempname(pwd())*".jld2"
        Constructor of transient solution with initial value and initial time.
        • in_memory: if true (default), data are kept in main memory, otherwise on disk (via JLD2)
        • keep_open: if true, disk file is not closed during the existence of the object
        • fname: file name for the disk file
        source
        VoronoiFVM.VectorOfDiskArrays — Method
        VectorOfDiskArrays(firstobj:AbstractArray;
+                  fname=tempname(pwd())*".jld2"
        Constructor of transient solution with initial value and initial time.
        • in_memory: if true (default), data are kept in main memory, otherwise on disk (via JLD2)
        • keep_open: if true, disk file is not closed during the existence of the object
        • fname: file name for the disk file
        source
        VoronoiFVM.VectorOfDiskArrays — Method
        VectorOfDiskArrays(firstobj:AbstractArray;
                    keep_open=true,
-                   fname= fname=tempname(pwd())*".jld2")
        Constructor of vector of arrays stored on disk (via JLD2).
        • keep_open: if true, disk file is not closed during the existence of the object
        • fname: file name for the disk file
        The disk file is automatically removed if the object is garbage collected.
        source
        
+                   fname= fname=tempname(pwd())*".jld2")

        Constructor of vector of arrays stored on disk (via JLD2).

        • keep_open: if true, disk file is not closed during the existence of the object
        • fname: file name for the disk file

        The disk file is automatically removed if the object is garbage collected.

        source
        diff --git a/dev/solver/index.html b/dev/solver/index.html index 8e6d2f2f4..931721861 100644 --- a/dev/solver/index.html +++ b/dev/solver/index.html @@ -1,16 +1,16 @@ -Built-in solver · VoronoiFVM.jl
        Edit on GitHub

        Built-in solver

        The package comes with a built-in solve method which solves stationary problems, simple homotopy embedding problems and transient problems via the implicit Euler method. This solver and its default parameters are tuned for robustness, possibly at the expense of solution speed. Careful tuning of the parameters, or – in the case of transient problems – the choice of the DifferentialEquations.jl solver can significantly improve the performance.

        CommonSolve.solve — Method
        solve(system; kwargs...)

        Solution method for VoronoiFVM.System. For using ODE solvers from DifferentialEquations.jl, see the VoronoiFVMDiffEq.jl package.

        Keyword arguments:

        • General for all solvers

          • inival (default: 0) : Array created via unknowns or number giving the initial value.
          • All elements of SolverControl can be used as kwargs.
          • control (default: nothing): Pass instance of SolverControl
          • params: Parameters (Parameter handling is experimental and may change)

        • Stationary solver: Invoked if neither times nor embed, nor tstep are given as keyword argument.

          • time (default: 0.0): Set time value.

          Returns a DenseSolutionArray or SparseSolutionArray

        • Embedding (homotopy) solver: Invoked if embed kwarg is given. Use homotopy embedding + damped Newton's method to solve stationary problem or to solve series of parameter dependent problems. Parameter step control is performed according to solver control data. kwargs and default values are:

          • embed (default: nothing ): vector of parameter values to be reached exactly

          In addition, all kwargs of the implicit Euler solver (besides times) are handled. Returns a transient solution object sol containing the stored solution(s), see TransientSolution.

        • Implicit Euler transient solver: Invoked if times kwarg is given. Use implicit Euler method + damped Newton's method to solve time dependent problem. Time step control is performed according to solver control data. kwargs and default values are:

          • times (default: nothing ): vector of time values to be reached exactly
          • pre (default: (sol,t)->nothing ): invoked before each time step
          • post (default: (sol,oldsol, t, Δt)->nothing ): invoked after each time step
          • sample (default: (sol,t)->nothing ): invoked after timestep for all times in times[2:end].
          • delta (default: (system, u,v,t, Δt)->norm(sys,u-v,Inf) ): Value used to control the time step size Δu

          If control.handle_error is true, if step solution throws an error, stepsize is lowered, and step solution is called again with a smaller time value. If control.Δt<control.Δt_min, solution is aborted with error. Returns a transient solution object sol containing the stored solution, see TransientSolution.

        • Implicit Euler timestep solver. Invoked if tstep kwarg is given. Solve one time step of the implicit Euler method.

          • time (default: 0): Set time value.
          • tstep: time step

          Returns a DenseSolutionArray or SparseSolutionArray

        source

        Solver control

        VoronoiFVM.SolverControl — Type
        SolverControl
+Built-in solver · VoronoiFVM.jl
        Built-in solver
        The package comes with a built-in solve method which solves  stationary problems, simple homotopy embedding problems and transient problems  via the implicit Euler method.  This solver and its default parameters are tuned for robustness, possibly at the expense of solution speed. Careful tuning of the parameters, or – in the case of transient problems – the choice of the DifferentialEquations.jl solver can significantly improve the performance.
        CommonSolve.solve — Method
        solve(system; kwargs...)
        Solution method for VoronoiFVM.System.   For using ODE solvers from DifferentialEquations.jl, see the VoronoiFVMDiffEq.jl package.
        Keyword arguments:
        • General for all solvers 
          • inival (default: 0) : Array created via unknowns or  number giving the initial value.
          • All elements of SolverControl can be used as kwargs.
          • control (default: nothing): Pass instance of SolverControl
          • params: Parameters (Parameter handling is experimental and may change)
        • Stationary solver: Invoked if neither times nor embed, nor tstep are given as keyword argument.
          • time (default: 0.0): Set time value.
          Returns a DenseSolutionArray or SparseSolutionArray
        • Embedding (homotopy) solver: Invoked if embed kwarg is given. Use homotopy embedding + damped Newton's method  to  solve stationary problem or to solve series of parameter dependent problems. Parameter step control is performed according to solver control data.  kwargs and default values are:
          • embed (default: nothing ): vector of parameter values to be reached exactly
          In addition,  all kwargs of the implicit Euler solver (besides times) are handled.   Returns a transient solution object sol containing the stored solution(s),  see TransientSolution.
        • Implicit Euler transient solver: Invoked if times kwarg is given. Use implicit Euler method  + damped   Newton's method  to  solve time dependent problem. Time step control is performed according to solver control data.  kwargs and default values are:
          • times (default: nothing ): vector of time values to be reached exactly
          • pre (default: (sol,t)->nothing ):  invoked before each time step
          • post  (default:  (sol,oldsol, t, Δt)->nothing ):  invoked after each time step
          • sample (default:  (sol,t)->nothing ): invoked after timestep for all times in times[2:end].
          • delta (default:  (system, u,v,t, Δt)->norm(sys,u-v,Inf) ):  Value  used to control the time step size Δu
          If control.handle_error is true, if step solution  throws an error, stepsize  is lowered, and  step solution is called again with a smaller time value. If control.Δt<control.Δt_min, solution is aborted with error. Returns a transient solution object sol containing the stored solution,  see TransientSolution.
        • Implicit Euler timestep solver.  Invoked if tstep kwarg is given. Solve one time step of the implicit Euler method.
          • time (default: 0): Set time value. 
          • tstep: time step
          Returns a DenseSolutionArray or SparseSolutionArray
        source
        Solver control
        VoronoiFVM.SolverControl — Type
        SolverControl
 SolverControl(;kwargs...)
-SolverControl(linear_solver_strategy, sys; kwargs...)
        Solver control parameter for time stepping, embedding, Newton method and linear solver control. All field names can be used as keyword arguments for solve(system::VoronoiFVM.AbstractSystem; kwargs...)
        Newton's method solves $F(u)=0$ by the iterative procedure $u_{i+1}=u_{i} - d_i F'(u_i)^{-1}F(u_i)$ starting with some initial value $u_0$, where $d_i$ is a damping parameter.
        For linear solver strategies, see VoronoiFVM.LinearSolverStrategy.
        • verbose::Union{Bool, String}: Verbosity control. A collection of output categories is given in a string composed of the following letters:
          • a: allocation warnings
          • d: deprecation warnings
          • e: time/parameter evolution log
          • n: newton solver log
          • l: linear solver log
          Alternatively, a Bool value can be given, resulting in
          • true: "neda"
          • false: "da"
          Switch off all output including deprecation warnings via verbose="". In the output, corresponding messages are marked e.g. via '[n]', [a] etc. (besides of '[l]')
        • abstol::Float64: Tolerance (in terms of norm of Newton update): terminate if $\Delta u_i=||u_{i+1}-u_i||_\infty <$ abstol.
        • reltol::Float64: Tolerance (relative to the size of the first update): terminate if $\Delta u_i/\Delta u_1<$ reltol.
        • maxiters::Int64: Maximum number of newton iterations.
        • tol_round::Float64: Tolerance for roundoff error detection: terminate if   $|\;||u_{i+1}||_1 - ||u_{i}||_1\;|/ ||u_{i}||_1<$ tol_round occurred max_round times in a row.
        • tol_mono::Float64: Tolerance for monotonicity test: terminate with error if $\Delta u_i/\Delta u_{i-1}>$ 1/tol_mono.
        • damp_initial::Float64: Initial damping parameter $d_0$. To handle convergence problems, set this to a value less than 1.
        • damp_growth::Float64: Damping parameter growth factor: $d_{i+1}=\min(d_i\cdot$ max_growth $,1)$. It should be larger than 1.
        • max_round::Int64: Maximum number of consecutive iterations within roundoff error tolerance The default effectively disables this criterion.
        • unorm::Function: Calculation of Newton update norm
        • rnorm::Function: Functional for roundoff error calculation
        • method_linear::Union{Nothing, LinearSolve.SciMLLinearSolveAlgorithm}: Solver method for linear systems (see LinearSolve.jl). If given nothing, as default are chosen (for Float64 calculations):
          • 1D:  KLUFactorization()
          • 2D:  SparspakFactorization()
          • 3D:  UMFPACKFactorization()
          SparspakFactorization() is the default choice for general number types. Users should experiment with what works best for their problem.
          For easy access to this functionality, see see also VoronoiFVM.LinearSolverStrategy.
        • reltol_linear::Float64:     Relative tolerance of iterative linear solver.
        • abstol_linear::Float64: Absolute tolerance of iterative linear solver.
        • maxiters_linear::Int64: Maximum number of iterations of linear solver
        • precon_linear::Union{Nothing, Function, ExtendableSparse.AbstractFactorization, LinearSolve.SciMLLinearSolveAlgorithm, Type}: Constructor for preconditioner for linear systems. This should work as a function precon_linear(A) which takes an AbstractSparseMatrixCSC (e.g. an ExtendableSparseMatrix) and returns a preconditioner object in the sense of LinearSolve.jl, i.e. which has an ldiv!(u,A,v) method. Useful examples:
          • ExtendableSparse.ILUZero
          • ExtendableSparse.Jacobi
          For easy access to this functionality, see see also VoronoiFVM.LinearSolverStrategy.
        • keepcurrent_linear::Bool: Update preconditioner in each Newton step ?
        • Δp::Float64: Initial parameter step for embedding.
        • Δp_max::Float64: Maximal parameter step size.
        • Δp_min::Float64: Minimal parameter step size.
        • Δp_grow::Float64: Maximal parameter step size growth.
        • Δt::Float64: Initial time step  size.
        • Δt_max::Float64: Maximal time step size.
        • Δt_min::Float64: Minimal time step size.
        • Δt_grow::Float64: Maximal time step size growth.
        • Δu_opt::Float64: Optimal size of update for time stepping and embeding. The algorithm tries to keep the difference in norm between "old" and "new" solutions  approximately at this value.
        • force_first_step::Bool: Force first timestep.
        • handle_exceptions::Bool: Handle exceptions during transient solver and parameter embedding. If true, exceptions in Newton solves are caught, the embedding resp. time step is lowered, and solution is retried. Moreover, if embedding or time stepping fails (e.g. due to reaching minimal step size), a warning is issued, and a solution is returned with all steps calculated so far.
          Otherwise (by default) errors are thrown.
        • store_all::Bool: Store all steps of transient/embedding problem:
        • in_memory::Bool: Store transient/embedding solution in memory
        • log::Any:    Record history
        • edge_cutoff::Float64: Edge parameter cutoff for rectangular triangles.
        • pre::Function: Function pre(sol,t) called before time/embedding step
        • post::Function: Function post(sol,oldsol,t,Δt) called after successful time/embedding step
        • sample::Function: Function sample(sol,t) to be called for each t in times[2:end]
        • delta::Function: Time step error estimator
        • tol_absolute::Union{Nothing, Float64}
        • tol_relative::Union{Nothing, Float64}
        • damp::Union{Nothing, Float64}
        • damp_grow::Union{Nothing, Float64}
        • max_iterations::Union{Nothing, Int64}
        • tol_linear::Union{Nothing, Float64}
        • max_lureuse::Union{Nothing, Int64}
        • mynorm::Union{Nothing, Function}
        • myrnorm::Union{Nothing, Function}
        source
        Linear Solver strategies
        VoronoiFVM.LinearSolverStrategy — Type
        VoronoiFVM.LinearSolverStrategy
        An linear solver strategy provides the possibility to construct SolverControl objects as follows:
            SolverControl(strategy,sys;kwargs...)
        , e.g.
            SolverControl(GMRESIteration(UMFPackFactorization(), EquationBlock()),sys;kwargs...)
        A linear solver strategy combines a Krylov method  with an (incomplete) factorization which by default is calculated from the linearization of the initial value of the Newton iteration.
        Currently available strategies are:
        Notable LU Factorizations are:
        Notable incomplete factorizations are:
        source
        VoronoiFVM.CGIteration — Type
        CGIteration(;factorization=UMFPACKFactorization())
-CGIteration(factorization)
        CG Iteration from Krylov.jl via LinearSolve.jl.
        source
        VoronoiFVM.BICGstabIteration — Type
        BICGstabIteration(;factorization=UMFPACKFactorization())
-BICGstabIteration(factorization)
        BICGstab Iteration from Krylov.jl via LinearSolve.jl.
        source
        VoronoiFVM.GMRESIteration — Type
        GMRESIteration(;factorization=ILUZeroFactorization(), memory=20, restart=true)
-GMRESIteration(factorization; memory=20, restart=true)
        GMRES Iteration from Krylov.jl via LinearSolve.jl.
        source
        Block preconditioning
        This feature is under development as of 1.6.
        VoronoiFVM.EquationBlock — Type
        EquationBlock()
        Equation-wise blocking. Can be combined with any preconditioner resp. factorization including direct solvers. In the moment, this requires a system with unknown_storage=:dense.
        source
        VoronoiFVM.PointBlock — Type
        PointBlock()
        Point-wise blocking. Currently only together with ILUZeroFactorization. This requires a system with unknown_storage=:dense.
        source
        History handling
        If log is set to true in solve, the history of newton iterations and  time/embedding steps is recorded and. For the respective previous solution step it can be obtained via history(system).
        VoronoiFVM.NewtonSolverHistory — Type
        mutable struct NewtonSolverHistory <: AbstractVector{Float64}
        History information for one Newton solve of a nonlinear system. As an abstract vector it provides the history of the update norms. See summary and details for other ways to extract information.
        • nlu::Int64:  number of Jacobi matrix factorizations
        • nlin::Int64:  number of linear iteration steps / factorization solves
        • time::Float64:  Elapsed time for solution
        • tasm::Float64:  Elapsed time for assembly
        • tlinsolve::Float64:  Elapsed time for linear solve
        • updatenorm::Any:  History of norms of $||u_{i+1}-u_i||$
        • l1normdiff::Any:  History of norms of $|\;||u_{i+1}||_1 - ||u_{i}||_1\;|/ ||u_{i}||_1$
        source
        VoronoiFVM.TransientSolverHistory — Type
        mutable struct TransientSolverHistory <: AbstractVector{NewtonSolverHistory}
        History information for transient solution/parameter embedding
        As an abstract vector it provides the histories of each implicit Euler/embedding step. See summary and details for other ways to extract information.
        • histories::Any:  Histories of each implicit Euler Newton iteration
        • times::Any:  Time values
        • updates::Any:  Update norms used for step control
        source
        Base.summary — Method
        summary(h::NewtonSolverHistory)
        Return named tuple summarizing history.
        source
        Base.summary — Method
        summary(h::TransientSolverHistory)
        Return named tuple summarizing history.
        source
        VoronoiFVM.details — Function
        details(h::NewtonSolverHistory)
        Return array of named tuples  with info on each iteration step
        source
        details(h::TransientSolverHistory)
        Return array of details of each solver step
        source
        Matrix extraction
        For testing and teaching purposes, one can obtain residual and linearization at a given vector of unknowns
        VoronoiFVM.evaluate_residual_and_jacobian — Function
        evaluate_residual_and_jacobian(system,u;
-                               t=0.0, tstep=Inf,embed=0.0)
        Evaluate residual and jacobian at solution value u. Returns a solution vector containing the residual, and an ExendableSparseMatrix containing the linearization at u.
        source
        Legacy API
        During the development of the code, a number of API variants have been developed which  are supported for backward compatibility.
        CommonSolve.solve! — Method
        solve!(solution, inival, system; 
+SolverControl(linear_solver_strategy, sys; kwargs...)
        Solver control parameter for time stepping, embedding, Newton method and linear solver control. All field names can be used as keyword arguments for solve(system::VoronoiFVM.AbstractSystem; kwargs...)
        Newton's method solves $F(u)=0$ by the iterative procedure $u_{i+1}=u_{i} - d_i F'(u_i)^{-1}F(u_i)$ starting with some initial value $u_0$, where $d_i$ is a damping parameter.
        For linear solver strategies, see VoronoiFVM.LinearSolverStrategy.
        • verbose::Union{Bool, String}: Verbosity control. A collection of output categories is given in a string composed of the following letters:
          • a: allocation warnings
          • d: deprecation warnings
          • e: time/parameter evolution log
          • n: newton solver log
          • l: linear solver log
          Alternatively, a Bool value can be given, resulting in
          • true: "neda"
          • false: "da"
          Switch off all output including deprecation warnings via verbose="". In the output, corresponding messages are marked e.g. via '[n]', [a] etc. (besides of '[l]')
        • abstol::Float64: Tolerance (in terms of norm of Newton update): terminate if $\Delta u_i=||u_{i+1}-u_i||_\infty <$ abstol.
        • reltol::Float64: Tolerance (relative to the size of the first update): terminate if $\Delta u_i/\Delta u_1<$ reltol.
        • maxiters::Int64: Maximum number of newton iterations.
        • tol_round::Float64: Tolerance for roundoff error detection: terminate if   $|\;||u_{i+1}||_1 - ||u_{i}||_1\;|/ ||u_{i}||_1<$ tol_round occurred max_round times in a row.
        • tol_mono::Float64: Tolerance for monotonicity test: terminate with error if $\Delta u_i/\Delta u_{i-1}>$ 1/tol_mono.
        • damp_initial::Float64: Initial damping parameter $d_0$. To handle convergence problems, set this to a value less than 1.
        • damp_growth::Float64: Damping parameter growth factor: $d_{i+1}=\min(d_i\cdot$ max_growth $,1)$. It should be larger than 1.
        • max_round::Int64: Maximum number of consecutive iterations within roundoff error tolerance The default effectively disables this criterion.
        • unorm::Function: Calculation of Newton update norm
        • rnorm::Function: Functional for roundoff error calculation
        • method_linear::Union{Nothing, LinearSolve.SciMLLinearSolveAlgorithm}: Solver method for linear systems (see LinearSolve.jl). If given nothing, as default are chosen (for Float64 calculations):
          • 1D:  KLUFactorization()
          • 2D:  SparspakFactorization()
          • 3D:  UMFPACKFactorization()
          SparspakFactorization() is the default choice for general number types. Users should experiment with what works best for their problem.
          For easy access to this functionality, see see also VoronoiFVM.LinearSolverStrategy.
        • reltol_linear::Float64:     Relative tolerance of iterative linear solver.
        • abstol_linear::Float64: Absolute tolerance of iterative linear solver.
        • maxiters_linear::Int64: Maximum number of iterations of linear solver
        • precon_linear::Union{Nothing, Function, ExtendableSparse.AbstractFactorization, LinearSolve.SciMLLinearSolveAlgorithm, Type}: Constructor for preconditioner for linear systems. This should work as a function precon_linear(A) which takes an AbstractSparseMatrixCSC (e.g. an ExtendableSparseMatrix) and returns a preconditioner object in the sense of LinearSolve.jl, i.e. which has an ldiv!(u,A,v) method. Useful examples:
          • ExtendableSparse.ILUZero
          • ExtendableSparse.Jacobi
          For easy access to this functionality, see see also VoronoiFVM.LinearSolverStrategy.
        • keepcurrent_linear::Bool: Update preconditioner in each Newton step ?
        • Δp::Float64: Initial parameter step for embedding.
        • Δp_max::Float64: Maximal parameter step size.
        • Δp_min::Float64: Minimal parameter step size.
        • Δp_grow::Float64: Maximal parameter step size growth.
        • Δt::Float64: Initial time step  size.
        • Δt_max::Float64: Maximal time step size.
        • Δt_min::Float64: Minimal time step size.
        • Δt_grow::Float64: Maximal time step size growth.
        • Δu_opt::Float64: Optimal size of update for time stepping and embeding. The algorithm tries to keep the difference in norm between "old" and "new" solutions  approximately at this value.
        • force_first_step::Bool: Force first timestep.
        • handle_exceptions::Bool: Handle exceptions during transient solver and parameter embedding. If true, exceptions in Newton solves are caught, the embedding resp. time step is lowered, and solution is retried. Moreover, if embedding or time stepping fails (e.g. due to reaching minimal step size), a warning is issued, and a solution is returned with all steps calculated so far.
          Otherwise (by default) errors are thrown.
        • store_all::Bool: Store all steps of transient/embedding problem:
        • in_memory::Bool: Store transient/embedding solution in memory
        • log::Any:    Record history
        • edge_cutoff::Float64: Edge parameter cutoff for rectangular triangles.
        • pre::Function: Function pre(sol,t) called before time/embedding step
        • post::Function: Function post(sol,oldsol,t,Δt) called after successful time/embedding step
        • sample::Function: Function sample(sol,t) to be called for each t in times[2:end]
        • delta::Function: Time step error estimator
        • tol_absolute::Union{Nothing, Float64}
        • tol_relative::Union{Nothing, Float64}
        • damp::Union{Nothing, Float64}
        • damp_grow::Union{Nothing, Float64}
        • max_iterations::Union{Nothing, Int64}
        • tol_linear::Union{Nothing, Float64}
        • max_lureuse::Union{Nothing, Int64}
        • mynorm::Union{Nothing, Function}
        • myrnorm::Union{Nothing, Function}
        source
        Linear Solver strategies
        VoronoiFVM.LinearSolverStrategy — Type
        VoronoiFVM.LinearSolverStrategy
        An linear solver strategy provides the possibility to construct SolverControl objects as follows:
            SolverControl(strategy,sys;kwargs...)
        , e.g.
            SolverControl(GMRESIteration(UMFPackFactorization(), EquationBlock()),sys;kwargs...)
        A linear solver strategy combines a Krylov method  with an (incomplete) factorization which by default is calculated from the linearization of the initial value of the Newton iteration.
        Currently available strategies are:
        Notable LU Factorizations are:
        Notable incomplete factorizations are:
        source
        VoronoiFVM.CGIteration — Type
        CGIteration(;factorization=UMFPACKFactorization())
+CGIteration(factorization)
        CG Iteration from Krylov.jl via LinearSolve.jl.
        source
        VoronoiFVM.BICGstabIteration — Type
        BICGstabIteration(;factorization=UMFPACKFactorization())
+BICGstabIteration(factorization)
        BICGstab Iteration from Krylov.jl via LinearSolve.jl.
        source
        VoronoiFVM.GMRESIteration — Type
        GMRESIteration(;factorization=ILUZeroFactorization(), memory=20, restart=true)
+GMRESIteration(factorization; memory=20, restart=true)
        GMRES Iteration from Krylov.jl via LinearSolve.jl.
        source
        Block preconditioning
        This feature is under development as of 1.6.
        VoronoiFVM.EquationBlock — Type
        EquationBlock()
        Equation-wise blocking. Can be combined with any preconditioner resp. factorization including direct solvers. In the moment, this requires a system with unknown_storage=:dense.
        source
        VoronoiFVM.PointBlock — Type
        PointBlock()
        Point-wise blocking. Currently only together with ILUZeroFactorization. This requires a system with unknown_storage=:dense.
        source
        History handling
        If log is set to true in solve, the history of newton iterations and  time/embedding steps is recorded and. For the respective previous solution step it can be obtained via history(system).
        VoronoiFVM.NewtonSolverHistory — Type
        mutable struct NewtonSolverHistory <: AbstractVector{Float64}
        History information for one Newton solve of a nonlinear system. As an abstract vector it provides the history of the update norms. See summary and details for other ways to extract information.
        • nlu::Int64:  number of Jacobi matrix factorizations
        • nlin::Int64:  number of linear iteration steps / factorization solves
        • time::Float64:  Elapsed time for solution
        • tasm::Float64:  Elapsed time for assembly
        • tlinsolve::Float64:  Elapsed time for linear solve
        • updatenorm::Any:  History of norms of $||u_{i+1}-u_i||$
        • l1normdiff::Any:  History of norms of $|\;||u_{i+1}||_1 - ||u_{i}||_1\;|/ ||u_{i}||_1$
        source
        VoronoiFVM.TransientSolverHistory — Type
        mutable struct TransientSolverHistory <: AbstractVector{NewtonSolverHistory}
        History information for transient solution/parameter embedding
        As an abstract vector it provides the histories of each implicit Euler/embedding step. See summary and details for other ways to extract information.
        • histories::Any:  Histories of each implicit Euler Newton iteration
        • times::Any:  Time values
        • updates::Any:  Update norms used for step control
        source
        Base.summary — Method
        summary(h::NewtonSolverHistory)
        Return named tuple summarizing history.
        source
        Base.summary — Method
        summary(h::TransientSolverHistory)
        Return named tuple summarizing history.
        source
        VoronoiFVM.details — Function
        details(h::NewtonSolverHistory)
        Return array of named tuples  with info on each iteration step
        source
        details(h::TransientSolverHistory)
        Return array of details of each solver step
        source
        Matrix extraction
        For testing and teaching purposes, one can obtain residual and linearization at a given vector of unknowns
        VoronoiFVM.evaluate_residual_and_jacobian — Function
        evaluate_residual_and_jacobian(system,u;
+                               t=0.0, tstep=Inf,embed=0.0)
        Evaluate residual and jacobian at solution value u. Returns a solution vector containing the residual, and an ExendableSparseMatrix containing the linearization at u.
        source
        Legacy API
        During the development of the code, a number of API variants have been developed which  are supported for backward compatibility.
        VoronoiFVM.SolverStrategies — Module
        SolverStrategies
        Only available in 1.5
        Please replace this functionality by the new strategy API in 1.6 as follows:
        direct_umfpack() = DirectSolver(UMFPACKFactorization())                            
+    tstep=Inf)
        Mutating version of solve(inival,system)
        source
        VoronoiFVM.SolverStrategies — Module
        SolverStrategies
        Only available in 1.5
        Please replace this functionality by the new strategy API in 1.6 as follows:
        direct_umfpack() = DirectSolver(UMFPACKFactorization())                            
 gmres_umfpack() = GMRESIteration(UMFPACKFactorization())                           
 gmres_eqnblock_umfpack() = GMRESIteration(UMFPACKFactorization(), EquationBlock()) 
 gmres_iluzero() = GMRESIteration(ILUZeroPreconditioner())                          
 gmres_eqnblock_iluzero() = GMRESIteration(ILUZeroPreconditioner(), EquationBlock())
-gmres_pointblock_iluzero() = GMRESIteration(ILUZeroPreconditioner(), PointBlock()) 
        source
        DifferentialEquations.jl solver
        This solver has been being outsourced into the glue package  VoronoiFVMDiffEq.jl
        
+gmres_pointblock_iluzero() = GMRESIteration(ILUZeroPreconditioner(), PointBlock())
        source

        DifferentialEquations.jl solver

        This solver has been being outsourced into the glue package VoronoiFVMDiffEq.jl

        diff --git a/dev/system/index.html b/dev/system/index.html index 1fd0d2b69..3da559009 100644 --- a/dev/system/index.html +++ b/dev/system/index.html @@ -1,5 +1,5 @@ -System · VoronoiFVM.jl
        Edit on GitHub

        System

        The computational grid required is assumed to correspond to a domain $\Omega=\cup_{r=1}^{n_\Omega} \Omega_r$

        Grids for VoronoiFVM are managed by the packages ExtendableGrids.jl and SimplexGridFactory.jl

        with boundary $\partial\Omega=\Gamma=\cup_{b=1}^{n_\Gamma} \Gamma_b$.

        The subdomains $\Omega_r$ are called "regions" and the boundary subdomains $\Gamma_b$ are called "boundary regions".

        On this complex of domains "lives" a number of species which are either attached to a number of regions or to a number of boundary regions.

        All these data, the matrix for the linear system and other things are hold together by a struct VoronoiFVM.System. This type is not exported to avoid name clashes.

        System constructors

        VoronoiFVM.System — Method
        System(grid; kwargs...)

        Create structure of type VoronoiFVM.System{Tv,Ti, Tm, TSpecMat<:AbstractMatrix, TSolArray<:AbstractMatrix} holding data for finite volume system solution.

        Parameters:

        • grid::ExtendableGrid: 1, 2 or 3D computational grid

        Keyword arguments:

        • species: vector of integer species indices. Added to all grid regions, avoiding the need to call enable_species! for this default case. If it is kept empty, species have be added to the system after creation via enable_species!.
        • unknown_storage: string or symbol. Information on species distribution is kept in sparse or dense matrices matrices and, correspondingly, the solution array is of type SparseSolutionArray or matrix, respectively. In the case of sparse unknown storage, the system matrix handles exactly those degrees of freedom which correspond to unknowns. However, handling of the sparse matrix structures for the bookkeeping of the unknowns creates overhead.
          • :dense : solution vector is an nspecies x nnodes dense matrix
          • :sparse : solution vector is an nspecies x nnodes sparse matrix
        • matrixindextype: Integer type. Index type for sparse matrices created in the system.
        • is_linear: whether the system is linear or not. If it is linear, only one Newton step is used to solve it.
        • assembly: either :cellwise (default) or :edgewise. Determine, how the assembly loop is organized. :cellwise means that the outer loop goes over grid cells (triangles, tetrahedra), and contributions to edge fluxes and node reactions are calculated for each cell. As a consequence, e.g. im 2D for all interior edges, flux functions are callled twice, once for each adjacent cell. Especially in 3D, this becomes a significant overhead. With :edgewise, geometry factors of these edges are pre-assembled, and the outer assembly loops go over all grid edges resp. nodes, still with separate calls if neigboring cells belong to different regions.
        Note

        It is planned to make :edgewise the default in a later version.

        Physics keyword arguments:

        • flux: Function. Flux between neighboring control volumes: flux(f,u,edge) or flux(f,u,edge,data) should return in f[i] the flux of species i along the edge joining circumcenters of neighboring control volumes. For species i,u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.

        • storage: Function. Storage term (term under time derivative): storage(f,u,node) or storage(f,u,node,data) It should return in f[i] the storage term for the i-th equation. u[i] contains the value of the i-th unknown.

        • reaction: Function. Reaction term: reaction(f,u,node) or reaction(f,u,node,data) It should return in f[i] the reaction term for the i-th equation. u[i] contains the value of the i-th unknown.

        • edgereaction: Function. Edge reeaction term: edgereaction(f,u,edge) or edgereaction(f,u,edge,data) It should return in f[i] the reaction term for the i-th equation. For species i,u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.

        • source: Function. Source term: source(f,node) or source(f,node,data). It should return the in f[i] the value of the source term for the i-th equation.

        • bflux: Function. Flux between neighboring control volumes on the boundary

        • breaction Function. Boundary reaction term: breaction(f,u,node) or breaction(f,u,node,data) Similar to reaction, but restricted to the inner or outer boundaries.

        • bcondition Function. Alias for breaction.

        • bsource: Function. Boundary source term: bsource(f,node) or bsource(f,node,data). It should return in f[i] the value of the source term for the i-th equation.

        • bstorage: Function. Boundary storage term: bstorage(f,u,node) or bstorage(f,u,node,data) Similar to storage, but restricted to the inner or outer boundaries.

        • generic_operator: Function. Generic operator generic_operator(f,u,sys). This operator acts on the full solution u of a system. Sparsity is detected automatically unless generic_operator_sparsity is given.

        • generic_operator_sparsity: Function defining the sparsity structure of the generic operator. This should return the sparsity pattern of the generic_operator.

        • nparams: number of parameters the system is depending on, and with respect to which the derivatives need to be obtained

        • data: User data (parameters). This allows to pass various parameters to the callback functions. If data is given, all callback functions should accept a last data argument. Otherwise, no data are passed explicitly, and constitutive callbacks can take parameters from the closure where the function is defined.

        • matrixtype: :default, :sparse, :tridiagonal, :banded

        source

        Adding species by species numbers

        VoronoiFVM.enable_species! — Method
        enable_species!(system,ispec,regions)

        Add species ispec to a list of bulk regions. Species numbers for bulk and boundary species have to be distinct. Once a species has been added, it cannot be removed.

        source
        VoronoiFVM.enable_species! — Method
        enable_species!(system; kwargs...)

        Keyword arguments:

        • species: Integer or vector of integers. Species to be added to the system.
        • regions: Vector of integers. Regions, where these species shall be added.If nothing, they are added to all species.

        Once a species has been added, it cannot be removed.

        source
        VoronoiFVM.enable_boundary_species! — Function
        enable_boundary_species!(system,ispec,regions)

        Add species ispec to a list of boundary regions. Species numbers for bulk and boundary species have to be distinct. Once a species has been added, it cannot be removed.

        source

        Handling boundary conditions

        Boundary conditions are handled in the bcondition callback passed to the system constructor. For being called in this callback, the following functions are available

        VoronoiFVM.boundary_dirichlet! — Method
         boundary_dirichlet!(y,u,bnode, args...; kwargs...)

        Keyword argument version:

        • species: species number. Default: 1
        • region: boundary region number. By default, all boundary regions.
        • value: value
        source
        VoronoiFVM.boundary_neumann! — Method
         boundary_neumann!(y,u,bnode, args...; kwargs...)

        Keyword argument version:

        • species: species number. Default: 1
        • region: boundary region number. By default, all boundary regions.
        • value: value
        source
        VoronoiFVM.boundary_robin! — Method
         boundary_robin!(y,u,bnode, args...; kwargs...)

        Keyword argument version:

        • species: species number. Default: 1
        • region: boundary region number. By default, all boundary regions.
        • factor: factor
        • value: value
        source
        VoronoiFVM.ramp — Function
           ramp(t; kwargs...)

        Ramp function for specifying time dependent boundary conditions

        Keyword arguments:

        • dt: Tuple: start and end time of ramp. Default: (0,0.1)
        • du: Tuple: values at start and end time. Default: (0,0)
        source

        Outflow boundary conditions

        These are characterized by the boutflow physics callback and and the outflowboundaries keyword argument in the system resp. physics constructor. See also the corresponding notebook

        VoronoiFVM.hasoutflownode — Function
        hasoutflownode(edge)

        Check if one node of the edge is situated on a boundary region listed in outflowboundaries, see [struct Physics].

        source
        VoronoiFVM.isoutflownode — Function
        isoutflownode(edge,inode)

        Check if inode (1 or 2) is an outflow node.

        source
        isoutflownode(edge,inode,irefgion)

        Check if inode (1 or 2) is an outflow node on boundary region iregion.

        source

        Allocation warnings

        The code checks for allocations in the assembly loop. Care has been taken to ensure that allocations in the assembly loop don't emerge from VoronoiFVM.jl code.

        If allocations occur in the assembly loop, they happen in the physics callbacks. The corresponding warnings can bee switched off by passing a verbosity strings without 'a' to the solver. If no data are allocated in the physics callbacks, these allocations are probably due to type instabilities in physics callbacks, see the the discussion here. Type instabilities can be debugged via the @time macro applied to expressions in a physics callback.

        The following cases provide some ideas where to look for reasons of the problem and possible remedies:

        Case 1: a parameter changes its value, and Julia is not sure about the type.

        eps=1.0
+System · VoronoiFVM.jl
        System
        The computational grid required is assumed to correspond to a domain $\Omega=\cup_{r=1}^{n_\Omega} \Omega_r$ 
        Grids for VoronoiFVM are managed by the packages ExtendableGrids.jl and SimplexGridFactory.jl
        with boundary  $\partial\Omega=\Gamma=\cup_{b=1}^{n_\Gamma} \Gamma_b$.
        The subdomains $\Omega_r$ are called "regions" and the boundary subdomains $\Gamma_b$ are called "boundary regions".
        On this complex of domains "lives"  a number of species which are either attached to a number of regions or to a number of boundary regions.
        All these data, the matrix for the linear system and other things are hold together by a struct VoronoiFVM.System.  This type is not exported to avoid name clashes.
        System constructors
        VoronoiFVM.System — Method
        System(grid; kwargs...)
        Create structure of type VoronoiFVM.System{Tv,Ti, Tm, TSpecMat<:AbstractMatrix, TSolArray<:AbstractMatrix}  holding data for finite volume system solution. 
        Parameters: 
        • grid::ExtendableGrid: 1, 2 or 3D computational grid
        Keyword arguments:
        • species: vector of integer species indices. Added to all grid regions, avoiding the need to call enable_species! for this default case.             If it is kept empty, species have be added to the system after creation via  enable_species!.
        • unknown_storage: string or symbol.     Information  on  species  distribution  is kept  in  sparse  or  dense   matrices matrices and, correspondingly, the  solution array is of type   SparseSolutionArray  or matrix,  respectively. In  the case  of sparse   unknown storage,  the system matrix  handles exactly those  degrees of   freedom which correspond to unknowns.  However, handling of the sparse   matrix  structures  for  the   bookkeeping  of  the  unknowns  creates   overhead.
          • :dense :  solution vector is an  nspecies x nnodes  dense matrix
          • :sparse :  solution vector is an nspecies x nnodes  sparse matrix
        • matrixindextype: Integer type. Index type for sparse matrices created in the system.
        • is_linear: whether the system is linear or not. If it is linear, only one Newton step is used to solve it.
        • assembly: either :cellwise (default) or :edgewise. Determine, how the assembly loop is organized.  :cellwise means that the outer loop goes over grid cells (triangles, tetrahedra), and contributions to  edge fluxes and node reactions are calculated for each cell. As a consequence, e.g. im 2D for all interior  edges, flux functions are callled twice, once for each adjacent cell. Especially in 3D, this becomes a significant  overhead. With :edgewise, geometry factors of these edges are pre-assembled, and the outer assembly loops  go over all grid edges resp. nodes, still with separate calls if neigboring cells belong to different regions.
        Note
        It is planned to make :edgewise the default in a later version.
        Physics keyword arguments:
        • flux: Function.     Flux between neighboring control volumes: flux(f,u,edge) or flux(f,u,edge,data)   should return in f[i] the flux of species i along the edge joining circumcenters   of neighboring control volumes.  For species i,u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.
        • storage: Function.  Storage term (term under time derivative): storage(f,u,node) or storage(f,u,node,data)    It should return in f[i] the storage term for the i-th equation. u[i] contains the value of   the i-th unknown.
        • reaction:  Function. Reaction term:  reaction(f,u,node) or reaction(f,u,node,data)    It should return in f[i] the reaction term for the i-th equation. u[i] contains the value of   the i-th unknown.
        • edgereaction:  Function. Edge reeaction term:  edgereaction(f,u,edge) or edgereaction(f,u,edge,data)    It should return in f[i] the reaction term for the i-th equation.  For species i,u[i,1] and u[i,2] contain the unknown values at the corresponding ends of the edge.
        • source:  Function. Source term: source(f,node) or source(f,node,data).   It should return the in f[i] the value of the source term for the i-th equation.
        • bflux:  Function. Flux between neighboring control volumes on the boundary
        • breaction Function.  Boundary reaction term:  breaction(f,u,node) or breaction(f,u,node,data)    Similar to reaction, but restricted to the inner or outer boundaries.
        • bcondition Function. Alias for breaction.
        • bsource: Function. Boundary source term: bsource(f,node) or bsource(f,node,data).   It should return in f[i] the value of the source term for the i-th equation.
        • bstorage: Function.  Boundary storage term: bstorage(f,u,node) or bstorage(f,u,node,data)    Similar to storage, but restricted to the inner or outer boundaries.
        • generic_operator: Function.  Generic operator  generic_operator(f,u,sys).    This operator acts on the full solution u of a system. Sparsity   is detected automatically  unless generic_operator_sparsity is given.
        • generic_operator_sparsity:  Function defining the sparsity structure of the generic operator.   This should return the sparsity pattern of the generic_operator.
        • nparams: number of parameters the system is depending on, and with respect to which the derivatives   need to be obtained
        • data:  User data (parameters).   This allows to pass various parameters to the callback functions. If data is given, all callback functions   should accept a last data argument. Otherwise, no data are passed explicitly, and constitutive callbacks can   take parameters from the closure where the function is defined.
        • matrixtype: :default, :sparse, :tridiagonal, :banded
        source
        Adding species by species numbers
        VoronoiFVM.enable_species! — Method
        enable_species!(system,ispec,regions)
        Add species ispec to a list of bulk regions. Species numbers for bulk and boundary species have to be distinct.  Once a species has been added, it cannot be removed.
        source
        VoronoiFVM.enable_species! — Method
        enable_species!(system; kwargs...)
        Keyword arguments:
        • species: Integer or vector of integers. Species to be added to the system.
        • regions: Vector of integers. Regions, where these species shall be added.If nothing, they are added to all species.
        Once a species has been added, it cannot be removed.
        source
        VoronoiFVM.enable_boundary_species! — Function
        enable_boundary_species!(system,ispec,regions)
        Add species ispec to a list of boundary regions. Species numbers for bulk and boundary species have to be distinct. Once a species has been added, it cannot be removed.
        source
        Handling boundary conditions
        Boundary conditions are handled in the  bcondition callback passed to the system constructor. For being called in this callback, the following  functions are available
        VoronoiFVM.boundary_dirichlet! — Method
         boundary_dirichlet!(y,u,bnode, args...; kwargs...)
        Keyword argument version:
        • species: species number. Default: 1
        • region: boundary region number. By default, all boundary regions.
        • value: value
        source
        VoronoiFVM.boundary_neumann! — Method
         boundary_neumann!(y,u,bnode, args...; kwargs...)
        Keyword argument version:
        • species: species number. Default: 1
        • region: boundary region number. By default, all boundary regions.
        • value: value
        source
        VoronoiFVM.boundary_robin! — Method
         boundary_robin!(y,u,bnode, args...; kwargs...)
        Keyword argument version:
        • species: species number. Default: 1
        • region: boundary region number. By default, all boundary regions.
        • factor: factor
        • value: value
        source
        VoronoiFVM.ramp — Function
           ramp(t; kwargs...)
        Ramp function for specifying time dependent boundary conditions
        Keyword arguments:
        • dt: Tuple: start and end time of ramp. Default: (0,0.1)
        • du: Tuple: values at start and end time. Default: (0,0)
        source
        Outflow boundary conditions
        These are characterized by the boutflow physics callback and  and the outflowboundaries keyword argument in the system resp. physics constructor. See also the  corresponding notebook
        VoronoiFVM.hasoutflownode — Function
        hasoutflownode(edge)
        Check if one node of the edge is situated on a boundary region listed in outflowboundaries, see [struct Physics].
        source
        VoronoiFVM.isoutflownode — Function
        isoutflownode(edge,inode)
        Check if inode (1 or 2) is an outflow node.
        source
        isoutflownode(edge,inode,irefgion)
        Check if inode (1 or 2) is an outflow node on boundary region iregion.
        source
        Allocation warnings
        The code checks for allocations in the assembly loop.  Care has been taken to ensure that allocations in the assembly loop don't emerge from VoronoiFVM.jl code.
        If allocations occur in the assembly  loop, they happen in the physics callbacks.  The corresponding warnings can bee switched off by passing a  verbosity strings  without  'a'  to the  solver.   If  no data  are allocated in the physics callbacks, these allocations are probably due to  type instabilities in physics callbacks, see the the discussion here.  Type instabilities can be debugged via the @time  macro applied to expressions in a physics callback.
        The following  cases provide some ideas  where to look for  reasons of the problem and possible remedies:
        Case 1: a parameter changes its value, and Julia is not sure about the type.
        eps=1.0
 
 flux(f,u,edge)
     f[1]=eps*(u[1,1]-[1,2])
@@ -12,27 +12,27 @@
 
 ... create etc ...
 
-x=solve(...)
        Remedy: rename e.g. x=solve() to sol=solve()
        Various tools
        VoronoiFVM.num_species — Function
        num_species(edge::VoronoiFVM.AbstractEdge) -> Any
+x=solve(...)
        Remedy: rename e.g. x=solve() to sol=solve()
        Various tools
        VoronoiFVM.num_species — Function
        num_species(edge::VoronoiFVM.AbstractEdge) -> Any
 
        Return number of species for edge
        source
        num_species(system)
 
        Number of species in system
        source
        num_species(a)
-
        Number of species (size of first dimension) of solution array.
        source
        VoronoiFVM.unknowns — Method
        unknowns(system; inival, inifunc)
+
        Number of species (size of first dimension) of solution array.
        source
        VoronoiFVM.unknowns — Method
        unknowns(system; inival, inifunc)
 
        Create a solution vector for system. If inival is not specified, the entries of the returned vector are undefined.
        source
        unknowns(impedance_system)
-
        Create a vector of unknowns of the impedance system
        source
        VoronoiFVM.unknowns — Method
        unknowns(Tu, system; inival, inifunc)
-
        Create a solution vector for system with elements of type Tu. If inival is not specified, the entries of the returned vector are undefined.
        source
        Base.map — Function
        map(inifunc, sys)
+
        Create a vector of unknowns of the impedance system
        source
        VoronoiFVM.unknowns — Method
        unknowns(Tu, system; inival, inifunc)
+
        Create a solution vector for system with elements of type Tu. If inival is not specified, the entries of the returned vector are undefined.
        source
        Base.map — Function
        map(inifunc, sys)
 
        Create a solution vector for system using the callback inifunc which has the same signature as a source term.
        source
        map(inival, sys)
-
        Create a solution vector for system using a constant initial value
        source
        Base.map! — Function
        map!(inifunc, U, system)
-
        Map inifunc onto solution array U
        source
        Base.reshape — Function
        reshape(v, system)
-
        Reshape vector to fit as solution to system.
        source
        Types
        VoronoiFVM.AbstractSystem — Type
        abstract type AbstractSystem{Tv<:Number, Tc<:Number, Ti<:Integer, Tm<:Integer}
        Abstract type for finite volume system structure.
        source
        VoronoiFVM.System — Type
        mutable struct System{Tv, Tc, Ti, Tm, TSpecMat<:(AbstractMatrix), TSolArray<:(AbstractMatrix)} <: VoronoiFVM.AbstractSystem{Tv, Tc, Ti, Tm}
        Structure holding data for finite volume system.
        source
        Legacy API
        VoronoiFVM.boundary_dirichlet! — Method
        boundary_dirichlet!(system, ispec, ibc, v)
-
        Set Dirichlet boundary condition for species ispec at boundary ibc:
        $u_{ispec}=v$ on $\Gamma_{ibc}$
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_dirichlet! — Method
          boundary_dirichlet!(system; kwargs...)
        Keyword argument version:
        • species: species number
        • region: region number
        • value: value
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_neumann! — Method
        boundary_neumann!(system, ispec, ibc, v)
-
        Set Neumann boundary condition for species ispec at boundary ibc:
        $\mathrm{flux}_{ispec}\cdot \vec n=v$ on $\Gamma_{ibc}$
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_neumann! — Method
          boundary_neumann!(system; kwargs...)
        Keyword argument version:
        • species: species number
        • region: region number
        • value: value
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_robin! — Method
        boundary_robin!(system, ispec, ibc, α, v)
-
        Set Robin boundary condition for species ispec at boundary ibc:
        $\mathrm{flux}_{ispec}\cdot \vec n + \alpha u_{ispec}=v$ on $\Gamma_{ibc}$
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_robin! — Method
          boundary_robin!(system; kwargs...)
        Keyword argument version:
        • species: species number
        • region: region number
        • factor: factor
        • value: value
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        Base.map! — Function
        map!(inifunc, U, system)
+
        Map inifunc onto solution array U
        source
        Base.reshape — Function
        reshape(v, system)
+
        Reshape vector to fit as solution to system.
        source
        Types
        VoronoiFVM.AbstractSystem — Type
        abstract type AbstractSystem{Tv<:Number, Tc<:Number, Ti<:Integer, Tm<:Integer}
        Abstract type for finite volume system structure.
        source
        VoronoiFVM.System — Type
        mutable struct System{Tv, Tc, Ti, Tm, TSpecMat<:(AbstractMatrix), TSolArray<:(AbstractMatrix)} <: VoronoiFVM.AbstractSystem{Tv, Tc, Ti, Tm}
        Structure holding data for finite volume system.
        source
        Legacy API
        VoronoiFVM.boundary_dirichlet! — Method
        boundary_dirichlet!(system, ispec, ibc, v)
+
        Set Dirichlet boundary condition for species ispec at boundary ibc:
        $u_{ispec}=v$ on $\Gamma_{ibc}$
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_dirichlet! — Method
          boundary_dirichlet!(system; kwargs...)
        Keyword argument version:
        • species: species number
        • region: region number
        • value: value
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_neumann! — Method
        boundary_neumann!(system, ispec, ibc, v)
+
        Set Neumann boundary condition for species ispec at boundary ibc:
        $\mathrm{flux}_{ispec}\cdot \vec n=v$ on $\Gamma_{ibc}$
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_neumann! — Method
          boundary_neumann!(system; kwargs...)
        Keyword argument version:
        • species: species number
        • region: region number
        • value: value
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_robin! — Method
        boundary_robin!(system, ispec, ibc, α, v)
+
        Set Robin boundary condition for species ispec at boundary ibc:
        $\mathrm{flux}_{ispec}\cdot \vec n + \alpha u_{ispec}=v$ on $\Gamma_{ibc}$
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.boundary_robin! — Method
          boundary_robin!(system; kwargs...)
        Keyword argument version:
        • species: species number
        • region: region number
        • factor: factor
        • value: value
        Info
        Starting with version 0.14, it is preferable to define boundary conditions within the bcondition physics callback
        source
        VoronoiFVM.viewK — Function
        viewK(
     edge::VoronoiFVM.AbstractEdge,
     u
 ) -> VoronoiFVM.VectorUnknowns
-
        Solution view on first edge node
        source
        VoronoiFVM.viewL — Function
        viewL(
     edge::VoronoiFVM.AbstractEdge,
     u
 ) -> VoronoiFVM.VectorUnknowns
-
        Solution view on second edge node
        source
        
+

        Solution view on second edge node

        source