Introduction to PDEs and Numerical Methods

Introduction to PDEs and Numerical Methods - WS2006/07

General Information

Lecturer Prof. H.G. Matties, PhD


Assistant Elmar Zander


Schedule Lecture: Wed 11:30-13:00 Uhr in room RZ 012 (Computing Center)



Exercises: Thu 12:15-13:00 Uhr in room RZ 012 (Computing Center)


Start First week of the semester


Prerequisites Basic courses up to the intermediate diploma


Target group Students of computer science, mathematics, natural or engineering sciences or guest students in their advanced study period, CSE students


Certificates Homework assignments and active participation in the exercises, tests, grading scheme


Office hours will be announced in the lecture


Literature:

A script for the lecture is available here.

Homework Assignments:

Here is a file (sample.zip) that shows you how to create EPS files from Matlab and how to combine them using LaTeX. Please download the file into your account, expand it with "unzip sample.zip" and read the README file for instructions. (Note: I assume here that you have a decent Unix/Linux installation, and are not running Windows or other crap, where things like this habitually don't work.)

E-Mail: If you want to submit your solutions electronically you can send them to wire-homeworks(at)tu-bs.de. Please do not send in DOC files, only PDF or PostScript. If you really think there is a need to compress your files, please use zip or tgz.

Note: From Matlab 7 (or 7.2) on there is a very nice "report" feature in matlab that let's you create nicely formatted reports with graphics and formulas etc. directly from a Matlab script. The default is to create an html report with jpeg graphics; if you change this to latex and eps (goto File/Preferences and then Editor/Debugger/Publishing) you can create your reports directly within matlab (File/Publish) with only one latex and dvips call on the command line.

Assignment 1 (Differential operators): assign1.ps, assign1.pdf

Assignment 2 (Integral theorems): assign2.ps, assign2.pdf
Note for exercise 3: Use Gauss' theorem as starting point.

Assignment 3: assign3.ps, assign3.pdf

Assignment 4: (Heat equation, analytical solutions) assign4.ps, assign4.pdf
Solution to the matlab exercises: ass4ex1.m, ass4ex2.m

Assignment 5: (Heat equation, numerical solution) assign5.ps, assign5.pdf, ass5ex1.m, ass5ex2.m, ass5ex3.m

Assignment 6: (Von Neumann Stability Analysis) assign6.ps, assign6.pdf

Assignment 7: (Wellposedness) assign7.ps, assign7.pdf

Assignment 8: (Implementation of a FEM program) assign8.ps, assign8.pdf

Links:

http://www-users.cs.umn.edu/%7Esaad/books.html
Two free books on the solution of large linear systems (with one chapter on the discretization of PDEs where most of those systems come from) and one on the solution of large eigenvalue problems.

http://en.wikipedia.org
Huge online encyclopedia with many good articles on mathematical topics (some sample topics vector calculus, heat equation, PDEs etc.

http://www.cfd-online.com
The online resource on computational fluid dynamics. Contains a wiki system on fluid dynamics, a huge collection of links to free resources on CFD and PDEs and numerical methods, etc.

Tests:

  • Here are the results of the second test: test-result.png.

  • Note: For the "big test" only those are eligible who have failed the small tests. It's not possible anymore to improve your mark here. The date is not fixed as yet, but will probably be at the end of April.