Introduction to PDEs and Numerical Methods

Introduction to PDEs and Numerical Methods

Introduction to PDEs and Numerical Methods - Winter Term 2010/2011 (INF-WR-04)

General Information

Lecturer Prof. Hermann G. Matthies, PhD


Assistant Dr. Alexander Litvinenko


Schedule Lecture: Wed 9:45-11:15, Fri 13:15-14:45 in room RZ 012 (Computing Center)



Exercises: Tue 11:30-13:00 in room RZ 012 (Computing Center)


Start 26.10.2010


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 office RZ120, every Mon. 9:30-11:00


Literature:

A script for the lecture is available here. The current revision is 1.1.

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 litvinen(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.

MATLAB code of some solutions of the assignments can be downloaded (zip-files) here: http://www.biblio.tu-bs.de/semapp/, click on "Prof. Hermann G. Matthies > Introduction to PDEs and Numerical Method" and then on the corresponding buttons "Volltext anzeigen"

PDE-2.

NEW!!!!! Announce! 25.01.2011 (Tue) will be PDE lecture, 26.01.2011 (Wed) and 28.01.2011 (Fri) will be practical exercises!, 01(Tue), 02(Wed), 04(Fri) Feb. 2011 will be lectures!!!, time and place as usual

NEW!!!!! EXAM: PDE1+2, 15 March, 10.00-12.00, RZ-012

The first part: Approximate contents of the course PDE-1

  • Motivation, examples of PDEs, their classification
  • Elliptic, parabolic and hyperbolic equations, ways of solving
  • Finite Difference Method (FDM) in 1D and 2D, implementation
  • Finite Element Method in 1D and 2D for linear elliptic boundary value problem, implementation
  • Iterative linear solvers (Gauss-Seidel, Jacobi, SOR methods)
  • Multigrid method

    • The second part: Approximate contents of the course PDE-2

  • Sets and lp spaces, Hilber spaces, norms, scalar products
  • Weak form and contraction
  • Lax-Milgram theorem
  • Sobolev spaces and weak derivatives
  • Application of embedding and trace theorems
  • (A Priori) Error estimation and quasi uniform meshes
  • Grid generation
  • Global a priori error estimation
  • A Posteriori error estimates
  • Dual weighted residual

    • Links:

    NEW !!! Repetition of a few Definitions and Facts (from H. G. Matthies)

    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.

    Software and Links

    Links to scientific computing related stuff:

    Matlab tutorials: