Math 226A Fall 2013

Math 266A Computational PDE

Meeting Information

• Room: RH 440R
• Day & time: M W F 10 - 11 am.

Project and Homework

• Homework 1: Exercises in Lecture Notes for Finite Difference Methods. Due date: Oct 10, 2013.
• Project 1: Finite Difference Method. Due date: Oct 18.

Use publish to summarize your project. A quick introduction on the publish function in matlab can be found in Publish MATLAB Code and Publishing Markup.

• Homework 2: Exerxise in Lecture Notes for Finite Element Methods. Due date: Oct 25.
• Project 2: Finite Element Method. Due date: Nov 4.
• Project 3: Fast Multipole Methods. Due date: Nov 18.
• Homework 3: Iterative Methods. Due date: Nov 25.
• Homework 4: Multigrid Methods. Due date: Dec 17.
• Final project: Multigrid Methods. Due date: Dec 17.

Syllabus

In Math 226 A, we shall focus on numerical solutions for the elliptic equations. Parabolic and hyperbolic equations will be discussed in 226 B and C, respectively. More precisely, we plan to cover the following topics:

• Finite element methods for linear elliptic equations
• Finite difference and finite volume methods
• Sobolev spaces and elliptic equations
• Fast solvers: Conjugate Gradient method and multigrid method
• Nonlinear elliptic equations
• Fast multiple methods

A pdf version of the syllabus can be downloaded from here.

References

Lecture Notes will be distributed in class. But the following books are good references for reading:

• Gilbert Strang. Computational Science and Engineering, Wellesley-Cambridge Press, 2007. Watch viedos in iTunes U.
• S. Larsson and V. Thomee, Partial Differential Equations with Numerical Methods, Springer, 2003.
• S.C. Brenner and L.R. Scott. The mathematical theory of finite element methods, vol. 15 of Texts in Applied Mathematics, Springer-Verlag, New York, second edition, 2002.

Grading

Your course grade will be determined by your cumulative average at the end of the term:

• 40% Homework
• 40% Matlab projects
• 20% Final Exam/Project

Lecture Notes

Welcome to send me your comments (e.g. typos, mistakes, notation inconsistence, suggestion, and even complains) on the lecture notes.

• Introduction
• Finite Difference Methods
• Programming of Finite Difference Methods
• Finite Element Methods
• Sobolev Spaces
• Programming of Finite Element Methods
• Finite Volume Methods
• Unified Error Analysis
• Fast Multipole Methods
• Iterative Methods, Subspace Correction Methods, and Auxiliary Space Methods
• Iterative Methods based on Krylov Space
• Multigrid Methods
• Programming of Multigrid Methods
• Convergence Theory of Multigrid Methods