Department of Computer Science
CPSC 520 : Numerical Methods for Time-Dependent Differential Equations
Instructor: U. M. Ascher
Contact: ascher at cs.ubc.ca,
Office: CS/CICSR 223
Lectures time and place: M W 11:00-12:30, ICCS 206
First lecture: Wednesday, September 5, 2012
Extra lecture: Friday, October 12, 2012
General course description
Tentative course outline
Grading scheme, consulting hours, etc.
Uri Ascher, Numerical
Methods for Evolutionary Differential Equations , SIAM, 2008.
There is a copy of this book in the reading room, on the reserved course
material shelf. An e-copy is available throught the UBC library.
Here is a copy of Chapter 16 of Ascher-Greif 2011: an easier version of our Chapter 2
There are two components in terms of deadlines:
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.
- A short presentation (about 10 minutes) during the last week of November
- Final project (writeup) due: Friday, December 14. .
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 select 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 text, extending some of the material that is mentioned but
not exhausted there. Potential topics extending the text include:
QuadTrees and OcTrees (Section 3.1)
Geometric Integration other than symplectic methods (e.g. Lie group methods; Chapter 6)
Spectral methods (Section 7.4)
Boussinesq equations (Chapter 7)
Nonlinear Schroedinger (Section 9.3)
Inverse problems involving time dependent PDEs (Chapter 9)
Additive methods; or exponential time differencing (Section 9.3)
Particle methods (e.g. cloth example); perhaps Smooth particle hydrodynamics (SPH, Section 7.5)
Semi-Lagrangian methods (Chapters 9 and 10)
Shocks in more than 1D (Chapter 10)
Any Chapter 11 topic
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.