Numerical Methods for PDEs
Spring Quarter 2019
|Professor Bob Guy
| R. J. LeVeque. Finite
Difference Methods for Ordinary and
Partial Differential Equations: Steady-State and Time-Dependent
Problems. SIAM, 2007.
Lloyd N. Trefethen, Spectral Methods
in MATLAB, SIAM, 2000.
Both books are available electronically from the library.
Homework and announcements will be posted here.
| MWF 3:10-4:00 in BAINER 1134
You are encouraged to talk with your classmates about homework
problems. However, you must do your own write-up and write your own
codes. All aspects of your write up must be clearly presented. Your
writing should be clear and grammatically correct. Your codes must be
thoroughly commented. All tables and figures must be appropriately
labeled. You will be graded on the quality of your presentation.
Prject abstracts due Friday, 4/19
Homework 1, due Wednesday, 4/17
Homework 2, due Friday, 5/3
Homework 3, due Wednesday, 5/15
| Wednesday, May 29th
1. Karry Wong
2. Art Kalb
| Friday, May 31st
1. Ojesh Koul
2. Frederico Zabaleta
| Monday, June 3rd
1. Raag Ramani
2. Andrew Chuen
| Wednesday, June 5th
1. Theo Eberts
2. Jiahe Chai
| Tuesday, June 11th, 1:00 PM
1. Shiva Murali
2. Aaron Burkhead
What we will cover
This coarse is part of the sequence 228A-C on numerical methods for
partial differential equations The third quarter (228C) will focus on
parabolic equations and spectral methods. The topics we will cover
this quarter are listed below.
- Introduction (Fourier transforms, derivation of conservation
laws, parabolic and hyperbolic PDEs)
- Numerical ODEs (briefly)
- Stability, accuracy, and convergence
- Von Neumann analysis
- Diffusion (reaction-diffusion) equation in multiple dimensions
- Nonrectangular geometry (logically quadrilateral grids and
- Spectral methods
Your grade will be
based on your homework assignments (60%) and project (40%). We will
likely have 2-3 homework assignments during this quarter.
This class will
require writing computer programs. You may use any language. If you
do not have a strong preference of language, I suggest that you
use MATLAB, because it is easy to use and very powerful. All
will be turned in and must be thoroughly commented.
As part of this class, you must complete a course project. This
will involve researching a topic in numerical PDEs or an application
which requires the numerical solution of PDEs. To complete the
project you are required to (1) give an in-class presentation, (2)
prepare a project report, and (3) attend other students'
presentations. You may work in groups of two or by
yourself. In the first few weeks of the class, you are required
to turn in a project proposal which describes your topic.
Please talk to me if you want some guidance in selecting a
topic. Below are some example topics. This list is not
meant to be exhaustive.
- Mesh generation
- Embedded boundaries
- Domain decomposition
- ENO/WENO methods
- Immersed interface method
- Stochastic DE/PDEs
- Adaptive mesh refinement (AMR)
- Compact finite differences
- Fast mulitpole method
- Boundary integral method
- A topic from your own research