## Math 226A Fall 2013 |

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

- 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.

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.

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.

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

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