Welcome

Welcome to CSCI-5636: Numerical Solution of Partial Differential Equations

Logistics

• Meeting Time: MWF 11:15-12:05 in ECCS 1B14

• Office hours: Choose a time

• Join in Zoom

• Canvas page

Activities

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.

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 with demo notebooks)

  • 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, How fast are nonsymmetric matrix iterations

  • Greenbaum, Pták, Strakoš, Any nonincreasing convergence curve is possible for GMRES

  • Embree, The tortoise and the hare restart GMRES