Math 226B Winter 2016

Math 266B Computational PDE

Meeting Information

• Room: RH 440R
• Day & time: M W F 10:00 - 10:50 am.
• Office hour: W F 11:00 - 12 am.

Project and Homework

• Project 1: Finite Element Method. Due date: Jan 25.
• Exercise 1: Finite Element Method. Due date: Feb 8.
• Exercise 2: Classical Iterative Method. Due date: Feb 22.
• Project 2: Multigrid Methods. Due date: Mar 7.
• Final Project: Nonlinear Poisson Boltzmann Equation. Due date: Mar 21.

Syllabus

In Math 226 B, we shall focus on numerical solutions for the elliptic equations. More precisely, we plan to cover the following topics:

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

References

Pdf files of lectures can be found in Lectures page. 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