Math 228C
Numerical Methods for PDEs
Spring Quarter 2019

Instructor:
   Office:
   Email:
   Phone:
   Office Hours:
 Professor Bob Guy
MSB 2136
guy@math.ucdavis.edu
754-9201
Tuesday 3-4
Wednesday 4-5
Friday 2-3


Textbook:
 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.


Webpage:
 http://www.math.ucdavis.edu/~guy/teaching/228c/
Homework and announcements will be posted here.


Class:
 MWF 3:10-4:00 in BAINER 1134



Homework
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

Presentation Schedule
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.

Grading
Your grade will be based on your homework assignments (60%) and project (40%). We will likely have 2-3 homework assignments during this quarter.

Programing
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 codes will be turned in and must be thoroughly commented.

Course Project
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