# TMA631 Projektkurs: partiella differentialekvationer

#### Spring 2001

#### Introduction

Since the course is a project based course the choice of projects are
critical. I will give some hints and suggestions for this here. This
is only to be taken as hints, You have full freedom to choose a
project that is of interest to You.
#### Requirements

The project should be done individually or in groups of two
persons. The project should be presented in a written report. In
addition to this You are required to give an oral presentation of the
project for the other students in the course.
#### Projects

The project should focus on numerically solving partial differential
equations. Below I will give some suggestions on suitable
projects. Since a majority of mathematical models in engineering leads
to partial differential equations almost any engineering application
can be considered. Regardless of which application You chose it might
be a good idea to solve a simple, linear scalar equation to begin
with. Poisson's equation in 2 or 3 dimensions is a good starting
point. A program that solves this can then be extended to handle
more complex systems.
Mesh generation and visualisation are needed to have a functional
program. Some of this could be obtained by using the Diffpack
software,
I can also assist you with other software for this purpose.

Project examples

- Heat conduction, compute the heating of a railway wheel sliding
on a rail. This is a problem of interest to railway engineers.
- Incompressible or compressible fluid flow, Make your own virtual wind-tunnel.
- Solid mechanics, Linear elasticity, Plasticity.
- Electromagnetics, solve Maxwells equations. Compute the
propagation of electromagnetic waves (radar applications, mobile
phone antennas).
- Sound propagation, simulate ultrasonic testing.
- The finite element method with higher order elements.
- Efficient solution of system equations using the Multigrid or Domain
decomposition method.
- Adaptive refinement using error estimates.

Please contact me for discussions, problem solving and hints. I can
also point out existing software which you can use in addition to Diffpack.

klassam@math.chalmers.se
Last modified: Sun Jan 14 18:47:00 MET 2001