Welcome to CSCI-5636: Numerical Solution of Partial Differential Equations
:::{admonition} Logistics
- Meeting Time: MWF 1:25-2:15pm in ECCS 1B14
- Office hours: Choose a time
- Join in Zoom
- Canvas page
- Please accept the Zulip invite on Canvas :::
% ::::{admonition} Activities % :::{list-table} % :header-rows: 1 % :widths: 30 70 % % * - Name % - Objectives % * - 2022-08-24-derivatives % - Use GitHub classroom and observe two kinds of numerical error: rounding error and discretization (aka. truncation) error. % * - 2022-09-19-blasius % - Solve a nonlinear PDE using spectral methods. Learn libraries and assess accuracy. % * - Community project % - This has three parts: community presentation, contribution, and % retrospective presentation about the contribution experience. The goal is to % build a deeper understanding of how open source communities function, what % metrics and implicit criteria are valued, and the design decisions and norms % that went into making libraries and applications successful. In the first stage, % you' ll survey the community, and in the second, you'll gain experience making a % specific contribution of your choosing. % ::: % ::::
:::{admonition} Resources
- SIAM Membership is free for CU students (30% discount on SIAM books)
- Lecture series
- Bangerth, Finite element methods in scientific computing course (focus on deal.II finite element library and C++)
- Books
- Driscoll and Braun, Fundamentals of Numerical Computation (free, in Julia)
- Myers, Van de Geijn, Van de Geijn, Linear Algebra: Foundations to Frontiers (free PDF and videos)
- LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations (CU students can download free from SIAM)
- LeVeque, Finite Volume Methods for Hyperbolic Problems and the Clawpack software.
- Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. (CU students can download free)
- Logg, Mardal, Wells, Automated Solution of Differential Equations by the Finite Element Method (The FEniCS Book). (free download)
- Trefethen, Spectral Methods in MATLAB. (CU students can download free from SIAM)
- Elman, Silvester, Wathen, Finite Elements and Fast Iterative Solvers with Applications in Incompressible Fluid Dynamics (CU students click "Full Text" to read online)
- Papers
- Roache, Code Verification by the Method of Manufactured Solutions
- Turk, Scaling a code in the human dimension arXiv
- Nachtigal, Reddy, Trefethen, {download}
How fast are nonsymmetric matrix iterations <downloads/NachtigalReddyTrefethen-HowFastAreNonsymmetricMatrixIterations-1992.pdf> - Greenbaum, Pták, Strakoš, {download}
Any nonincreasing convergence curve is possible for GMRES <downloads/GreenbaumPtakStrakos-AnyNonincreasingConvergenceCurvePossibleGMRES-1996.pdf> - Embree, {download}
The tortoise and the hare restart GMRES <downloads/Embree-TheTortoiseAndTheHareRestartGMRES-2003.pdf>:::