TMA632 Project course PDE 05/06, 5 credits
Differential equations, ODEs or PDEs, can be solved by general methods, and in this course you will learn how such a general method can be constructed. You will use the FEniCS free software platform, which is an implementation of such a method, to solve a problem of your choice.
You are free to choose your own project. The work is presented at the end of the course in the form of a report and a short seminar. Suggestions for projects will be given, some more oriented towards programming, and some towards mathematical modeling.
At the beginning of the course, there will be a short series of lectures, giving a brief overview of some important issues related to numerical approximation of PDEs, including the finite element method, and issues related to computer implementation of such algorithms. We will also discuss Python (perhaps also some C++) programming in Unix (or GNU/Linux) environments.
You are encouraged to find your own literature on your subject of interest, but a good starting point is Computational Differential Equations by Eriksson, Estep, Hansbo, and Johnson, or Applied Mathematics: Body and Soul by Eriksson, Estep, and Johnson.
Some relevant papers and chapter excerpts:
- Laplacian Models
- Navier-Stokes: Quick and Easy
- Compressible Flow (p. 37- for compressible Euler in 2d/3d)
- A Compiler for Variational Forms (paper on FFC describing factorization of reference tensor)
The literature list will be extended with relevant chapter excerpts from other PDE/FEM books during the course.
In Python you could use the documentation available online at www.python.org. A tutorial for the Numeric module is available at the OnLamp site.
A tutorial for debugging in Python by Stephen Ferg.
In C++ you could start with Thinking in C++ by Eckel, which is available on the net, C++ Primer by Lippman, which is a bit old but good, or C++ direkt by Skansholm , if you read swedish. A good reference book is The C++ Programming Language by Stroustrup.
All groups have to give two mandatory project reports in study week 4 and week 6. The time and place are the same as the consultation time, i.e. 13-15 Monday or 10-12 Friday. Please send an e-mail to book time.