Math 275: Topics in Applied Mathematics, Fall 2005


Lecture: MWF 12:10-1:00 pm, 75 Evans

Instructor: Jon Wilkening, wilken@math.berkeley.edu

Course webpage: http://math.berkeley.edu/~wilken/275.F05

Office: 1091 Evans, (510) 643-7990 or (510) 486-7006.

Office hours: Monday 1:00-2:00, Thursday 3:00-4:00


Course Description

Prerequisites: Advanced Calculus

Texts:
Dietrich Braess, Finite Elements: Theory, fast solvers, and applications in solid mechanics.
C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow.

Grading:
I will assign 5 straightforward programming projects during the semester. Students are expected to complete 3 of them according to their interests. They may work in groups of one, two or three and use any convenient programming language (Matlab, C, C++, Fortran, Java...).

Content:
In this course, we will study fundamental aspects of the finite element and boundary integral methods for solving elliptic equations, especially the Poisson equation, the equations of elasticity, and the Stokes equations. I will also cover more advanced topics including mixed finite element methods, corner singularities, least squares finite elements, the calculus of variations, shape optimization, the Navier-Stokes equations (in the velocity-pressure and vorticity-stream formulations), fast linear solvers, elliptic grid generation, and various competing methods such as the immersed interface and immersed boundary methods. My goal is to present a wide array of interesting numerical methods for solving partial differential equations which aren't normally covered in Math 228b.