Math951 - Numerical PDEs II
Professor: Jianliang Qian
Office: A306 Wells Hall
Lectures: TTH 10:20-11:40
Location: C216 WH
Office Hours: TTH4pm-5pm and by appointment
Course Website: http://www.math.msu.edu/~qian/951.12s/index951.html
Description and Contents
This course will cover direct methods for solving PDEs, including finite-difference (FD) and finite-element (FE)
methods in general. The model equations consist of Poisson, heat, and wave equations. Various analysis tools
will be covered. However, the main focus of the course this semester will be on FDM and FEM for wave equations. Specifically, we will roughly cover the following:
- Background related to functional analysis
- FDM for hyperbolic equations
- FEM for elliptic equations
- FEM for hyberbolic equations
- Some state-of-the-art FEMs if time allows
- G. Cohen, Higher-order numerical methods for transient wave equations, Springer, 2002.
- P. G. Ciarlet, The finite element methods for elliptic equations, SIAM, 2002.
- D. Braess, Finite elements, Cambridge, 2001.
- P. Monk, Finite Element Methods for Maxwell's Equations, Clarendon Press, Oxford, 2003.
Homework and Projects
- This will be a computationally intensive course, including programming and written assignments.
- The computational problems will utilize MATLAB, but other languages (Fortran, C, C++, etc)
are acceptable as well.
- Homework due in class. No late homework accepted.
- Final Exam/Final Project: TBA.
Grading based on
- Class participation (10%), assignments (60%), Final Exam/Project (30%).
- 4.0: 90% - 100%; 3.5: 80% - 89%; 3.0: 70% - 79%; 2.5: 60% - 69%; 2.0: less than 60%.