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Documenter.jl committed Jan 5, 2025
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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2024-12-13T14:57:11","documenter_version":"1.8.0"}}
{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-05T21:28:41","documenter_version":"1.8.0"}}
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return false # We don't want to add new stopping conditions
end

(x, stats) = gmres(A, b, callback = gmres_callback)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../matrix_free/">« Matrix-free operators</a><a class="docs-footer-nextpage" href="../custom_workspaces/">Custom workspaces »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 13 December 2024 14:57">Friday 13 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
(x, stats) = gmres(A, b, callback = gmres_callback)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../matrix_free/">« Matrix-free operators</a><a class="docs-footer-nextpage" href="../custom_workspaces/">Custom workspaces »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 5 January 2025 21:28">Sunday 5 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
4 changes: 2 additions & 2 deletions dev/custom_workspaces/index.html
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residuals: []
Aresiduals: []
κ₂(A): []
timer: 782.28ms
timer: 647.19ms
status: solution good enough given atol and rtol
)</code></pre><pre><code class="language-julia hljs"># The exact solution is u(x,y) = sin(πx) * sin(πy)
u_star = [sin(π * i * Δx) * sin(π * j * Δy) for i=1:Nx, j=1:Ny]
norm(u_sol.data[1:Nx, 1:Ny] - u_star, Inf)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2.035659636356879e-5</code></pre><h3 id="Conclusion"><a class="docs-heading-anchor" href="#Conclusion">Conclusion</a><a id="Conclusion-1"></a><a class="docs-heading-anchor-permalink" href="#Conclusion" title="Permalink"></a></h3><p>Implementing a 2D Poisson equation solver with <code>HaloVector</code> improves code clarity and efficiency. Custom indexing with <code>OffsetArray</code> streamlines halo region management, eliminating boundary checks within the core loop. This approach reduces branching, yielding faster execution, especially on large grids. <code>HaloVector</code>&#39;s flexibility also makes it easy to extend to 3D grids or more complex stencils.</p><div class="admonition is-info"><header class="admonition-header">Info</header><div class="admonition-body"><p><a href="https://github.com/CliMA/Oceananigans.jl">Oceananigans.jl</a> uses a similar strategy with its <code>Field</code> type, efficiently solving large linear systems with Krylov.jl.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../callbacks/">« Callbacks</a><a class="docs-footer-nextpage" href="../tips/">Performance tips »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 13 December 2024 14:57">Friday 13 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
norm(u_sol.data[1:Nx, 1:Ny] - u_star, Inf)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">2.035659636356879e-5</code></pre><h3 id="Conclusion"><a class="docs-heading-anchor" href="#Conclusion">Conclusion</a><a id="Conclusion-1"></a><a class="docs-heading-anchor-permalink" href="#Conclusion" title="Permalink"></a></h3><p>Implementing a 2D Poisson equation solver with <code>HaloVector</code> improves code clarity and efficiency. Custom indexing with <code>OffsetArray</code> streamlines halo region management, eliminating boundary checks within the core loop. This approach reduces branching, yielding faster execution, especially on large grids. <code>HaloVector</code>&#39;s flexibility also makes it easy to extend to 3D grids or more complex stencils.</p><div class="admonition is-info"><header class="admonition-header">Info</header><div class="admonition-body"><p><a href="https://github.com/CliMA/Oceananigans.jl">Oceananigans.jl</a> uses a similar strategy with its <code>Field</code> type, efficiently solving large linear systems with Krylov.jl.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../callbacks/">« Callbacks</a><a class="docs-footer-nextpage" href="../tips/">Performance tips »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 5 January 2025 21:28">Sunday 5 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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[Left preconditioning] Residual norm: 3.2e-07
[Left preconditioning] Number of iterations: 9
[Right preconditioning] Residual norm: 7.8e-06
[Right preconditioning] Number of iterations: 8</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../trimr/">« TriMR</a><a class="docs-footer-nextpage" href="../dqgmres/">DQGMRES »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 13 December 2024 14:57">Friday 13 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
[Right preconditioning] Number of iterations: 8</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../trimr/">« TriMR</a><a class="docs-footer-nextpage" href="../dqgmres/">DQGMRES »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 5 January 2025 21:28">Sunday 5 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
4 changes: 2 additions & 2 deletions dev/examples/block_gmres/index.html
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residuals: []
Aresiduals: []
κ₂(A): []
timer: 253.15ms
timer: 257.24ms
status: solution good enough given atol and rtol
Relative residual: 6.8e-09</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../dqgmres/">« DQGMRES</a><a class="docs-footer-nextpage" href="../cgne/">CGNE »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 13 December 2024 14:57">Friday 13 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Relative residual: 6.8e-09</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../dqgmres/">« DQGMRES</a><a class="docs-footer-nextpage" href="../cgne/">CGNE »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 5 January 2025 21:28">Sunday 5 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
4 changes: 2 additions & 2 deletions dev/examples/car/index.html
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residuals: []
Aresiduals: []
κ₂(A): []
timer: 19.83ms
timer: 19.17ms
status: solution good enough given atol and rtol
Relative residual: 1.5e-08</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../cg/">« CG</a><a class="docs-footer-nextpage" href="../cg_lanczos_shift/">CG-LANCZOS-SHIFT »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 13 December 2024 14:57">Friday 13 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Relative residual: 1.5e-08</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../cg/">« CG</a><a class="docs-footer-nextpage" href="../cg_lanczos_shift/">CG-LANCZOS-SHIFT »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Sunday 5 January 2025 21:28">Sunday 5 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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