COURSE DESCRIPTION
Syllabus
Basic
course policies including attendance and grief absence
Finite difference methods for time dependent problems:
accuracy and stability, wave equations, parabolic equations.
A brief introduction to finite element method.
Solving linear systems: iterative methods, conjugate gradients and multigrid.
Prerequisites: MA 511 and MA 514 (or similar ones)
LECTURE NOTES (updated on Mar 29)
Reference Books (for those with *, online access available via Purdue Library):
- Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems*
- John C. Strikwerda, Finite Difference Schemes and Partial Differential Equations*
- G. Strang, Computational Science and Engineering
- Trefethen and David Bau, Numerical Linear Algebra
- Gustafsson, Bertil; Kreiss, Heinz-Otto; Oliger, Joseph, Time Dependent Problems and Difference Methods
- U. M. Ascher; Linda Ruth Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
- Demmel, James W., Applied Numerical Linear Algebra*
- Y. Saad, Iterative Methods for Sparse Linear Systems*
- Lloyd N. Trefethen, Spectral Methods in MATLAB*
Problem Sets
HOMEWORK
# 1 due on Feb 5 Poisson1D_Dirichlet.m
Poisson2D_Neumann.m
HOMEWORK#2 due on Feb 21 Kepler_reference_q.mat
Demo code to draw ODE
solver stability region
HOMEWORK#3 due on Mar 19
HOMEWORK#4 due on Mar 28
HOMEWORK#5 due on April 11
Schedule
Note: The schedule is subject to change. Check back for changes and updates
| Date | Topic |
|---|---|
| Jan 8 Tue |
Introduction. 1D Poisson Equation. |
| Jan 10 Th |
2D Poisson Equation. |
| Jan 15 Tue |
Introduction to ODE. |
| Jan 17 Th |
ODE Solvers. |
| Jan 22 Tue |
2D Poisson |
| Jan 24 Th |
Fourier Transform |
| Jan 29 Tue |
wellposedness |
| Jan 31 Th |
wellposedness |
| Feb 5 Tue |
ODE |
| Feb 7 Th |
Runge-Kutta |
| Feb 12 Tue |
Runge-Kutta; Multi-Step Method |
| Feb 14 Th |
Multi-Step Method |
| Feb 19 Tue |
wellposedness of hyperbolic equations |
| Feb 21 Th |
definition of stability for time-dependent problems |
| Feb 26 Tue |
HW Solutions |
| Feb 28 Th |
linear time-dependent PDE |
| Mar 5 Tue |
linear time-dependent PDE |
| Mar 7 Th |
stability of leap-frog
schemes |
| Mar 12 Tue |
No Class. Spring Vacation. |
| Mar 14 Th |
No Class. Spring Vacation. |
| Mar 19 Tue |
stability of hyperbolic systems |
| Mar 21 Th |
Jacobi/Gauss Seidel/SOR iterations; Steepest Descent |
| Mar 26 Tue |
Conjugate Gradient |
| Mar 28 Th |
HW#4 Solutions |
| Apr 2 Tue |
Preconditioned CG; Mutligrid v-cycle |
| Apr 4 Th |
Mutligrid |
| Apr 9 Tue |
Multigrid; Sobolev space |
| Apr 11 Th |
Finite element method |
| Apr 16 Tue |
Finite element method |
| Apr 18 Th |
Finite element method |
| Apr 23 Tue |
Review |
| Apr 25 Tue |
Review |
