Fall 2007

Instructor: U. M. Ascher

Contact: ascher at cs.ubc.ca, 604-822-4907

Office: CS/CICSR 223

Lectures time and place: T Th 3:30-5:00, DMP 101

First lecture: Tuesday, September 11

General course description

Tentative course outline

Grading scheme, consulting hours, etc.

Assignments

• Assignment 1: Due Thu, Sept. 27, 2007.

  Do Exercises 1.3, 1.5, 1.6, 1.7 and 1.10.

• Assignment 1: solution

• Assignment 2: Due Thu, Oct. 11, 2007.

  Do Exercises 2.2, 2.3, 2.8, 2.9 and 2.11.

  Please check the version that is currently on the notes web site for the correct numbers.

• Assignment 2: solution

• Assignment 3: Due Thu, Nov. 2, 2007.

  Do Exercises 3.2, 3.3, 4.2, 4.9, 5.2 and 5.4.

  Please check the version that is currently on the notes web site for the correct numbers.

• Assignment 3: solution

• Assignment 4: Due Tue, Nov. 20, 2007.

  Do four (4) Exercises of your choice out of 6.1, 6.5, 6.6, 7.4 and 7.5.

  Please check the version that is currently on the notes web site for the correct numbers.

• Assignment 4: solution

Midterm

Thursday, October 25, 2007

Final project

There are two components in terms of deadlines:
• A short presentation (10 minutes) during the last week of November
• Final project (writeup) due: Monday December 17 .
The combined project weight is 50%, so this should give you a rough idea of the intended scope: the actual work is basically like the four assignments combined.

Whatever you choose your project to be it should connect to the course material: ask yourself if you could do the project of your choice without any knowledge gained in the course, and if the answer is positive then choose another project. Check with me if unsure.

Your project can be on anything you choose; say, something connected to your research direction. There are also lots of project topics that suggest themselves upon reading the course notes, extending some of the material that is mentioned but not exhausted there. Potential topics from the notes include:

• QuadTrees and OcTrees (Section 3.1)
• Geometric Integration other than symplectic methods (e.g. Lie group methods; Chapter 6)
• Spectral methods (the new Section 7.4)
• Boussinesq equations (Chapter 7)
• Nonlinear Schroedinger (Section 9.3)
• Inverse problems involving time dependent PDEs (Chapter 9)
• Particle methods (e.g. cloth example); perhaps Smooth particle dynamics (SPH, Section 7.5)
• Semi-Lagrangian methods (Chapters 9 and 10)
• Shocks in more than 1D (Chapter 10)
• Any Chapter 11 topic

Web resources:

• You can access various on-line guides to MATLAB: see for instance the cpsc303 web page as well as Ian Mitchell's and Kevin Murphy's helpers.
• Trefethen notes - not quite a textbook, but available online.

Software

• CLAWPACK - A package for hyperbolic conservation laws written by R. LeVeque et. al.
• Toolbox of Level Set Methods - A package for level set methods, generally following Osher-Fedkiw, written by Ian Mitchell.

Demos