CME 306/CS 237C : Numerical Solution of Partial Differential Equations

Spring 2006

Lectures: Monday and Wednesday, 2:15-3:30, in Terman Engineering, Terman Auditorium.
Discussion sections (optional): Friday, 3:30-4:45, Gates B12
Instructor: Ron Fedkiw (fedkiw@cs.stanford.edu), Gates 207.
TA: Tamar Shinar (shinar@stanford.edu), Gates 209. Office hours: Tuesdays, 2 pm - 3 pm

Course Announcements

Date	Announcement

6/02/2006	The final exam will be Friday, June 9, 12:15 pm -3:15 pm in the regular room. Please see details below in the Exams and Grading sections.
6/02/2006	The extra credit assignments will be due Thursday, June 15.
4/17/2006	Exam I will be on Monday, May 1. It will cover Lectures 1-7
4/17/2006	Exam II will be on Wednesday, June 7. It will cover Lectures 8-16
4/17/2006	Homeworks should be submitted on the due date by 11 am. They can be submitted in hard copy or by email to the TA. There is box located outside the TA's office where homeworks can be dropped.
4/17/2006	The TA's office hours are Tuesday from 2 pm - 3 pm. If you cannot come at that time, you can also arrange to drop by some other time, or see the TA or the instructor following the lectures.

Recommended Texts

Finite Volume Methods for Hyperbolic Problems, by Randall J. LeVeque, Cambridge University Press 2002

here

Finite Difference Schemes and Partial Differential Equations (2nd ed.), by John C. Strikwerda, SIAM 2004

Additional Resources

Level Set Methods and Dynamic Implicit Surfaces, by Stanley Osher and Ronald Fedkiw, Springer 2003

here

Robert D. Guy, Aaron L. Fogelson, Stability of approximate projection methods on cell-centered grids. J. Comput. Phys. 203, 517-538.
CS 205 notes on Poisson's equation
Selle, A., Rasmussen, N. and Fedkiw, R., "A Vortex Particle Method for Smoke, Water and Explosions", SIGGRAPH 2005, ACM TOG 24, (2005).
An example of using ENO-LLF to solve a hyperbolic system here.

Topics

Hyperbolic problems:
- Wave equation: multiple spatial dimensions, upwinding, CFL restriction, high order accuracy in space and time
- Burgers equation: nonlinear behavior. shocks and rarefactions, conservation laws, flux form differencing
- Compressible Euler equations: systems, eigenvalues and eigenvectors
Mixed Hyperbolic, Parabolic, Elliptic:
- Incompressible Flow: hyperbolic convection terms, parabolic viscous terms, elliptic pressure solver to enforce incompressibility
- Heat flow

Homework Assignments

There will be a problem set assigned each week. Homeworks should be submitted by 11 am on the due date. Solutions to the assigned problems will be provided and the homework will be graded in coarse increments of 0, ½, 1, 1 ½ or 2 points. A sample midterm will be assigned in lieu of normal problems the week before each midterm and graded coarsely out of 3 points. The solutions will be posted at the time the homework is due and no late homework will be accepted afterwards.

Homework	Date due	pdf	tex	Solution
1	April 13	pdf	tex	pdf
2	April 20	pdf	tex	pdf
3	April 27	pdf	tex	pdf
4	May 4	pdf	tex	pdf
5	May 11	pdf	tex	pdf
6	May 18	pdf	tex	pdf
7	May 25	pdf	tex	pdf
8	June 1	pdf	tex	pdf
9	June 8	pdf	tex figure

Extra Credit Assignments

Burgers equation [PDF]
Sod's shock tube [PDF]
Incompressible [PDF]

Examination

There will be two in-class midterm examinations, dates given below. Additionally there will be an optional cumulative final. If you choose not to take the final, your final exam grade will be determined by averaging your two midterm scores.

Exam I: Monday, May 1, lectures 1-7, homeworks 1-4
Exam II: Wednesday, June 7, lectures 8-16, homeworks 5- . Solutions (problems 1-9)
Final (optional): Friday, June 9, 12:15-3:15 pm, comprehensive

The final will consist of two parts, corresponding roughly midterm I and midterm II. Students can take either or both parts of the exam.

Qual

Grading

The grading options are summarized in the table below.

Grading Options	Homework	Midterm I	Midterm II	Final Part I	Final Part II
Option 1	20%	40%	40%	0%	0%
Option 2	20%	20%	40%	20%	0%
Option 3	20%	40%	20%	0%	20%
Option 4	20%	20%	20%	20%	20%