TMA631 Projektkurs: partiella differentialekvationer

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