65-532 * Seminar on Numerical Methods for PDEs - Theory and Implementation

Lehrende: Prof. Dr. Jörn Behrens; Dr. Konrad Simon

Veranstaltungsart: Seminar

Anzeige im Stundenplan: M-Sem

Semesterwochenstunden: 2

Unterrichtssprache: Deutsch

Min. | Max. Teilnehmerzahl: 5 | 14

Kommentare/ Inhalte:
Language of instruction: English


Students are advised and encouraged to seek counseling with the tutor during their project implementation. Please make an appointment by writing me an email.


What is the seminar about?

Partial differential equations (PDE) appear in many situations in mathematics, physics, biology, engineering and computer science -- just to mention a few. PDE theory gives us analytical tools to assess the qualitative bahvior of solutions. However, in most practically relevant applications it is important to also quantify solutions to very complicated PDEs. Numerical methods are used to find approximate solutions to such equations but their choice highly depends on the problem at hand.

In this seminar the students will get aquainted with

• Examples for PDE and related problems from different disciplines in sciences
  
• A set of numerical methods to solve PDE problems
  
• Tools to implement numerical methods, i.e., programming languages
  
• A basic introduction to possible workflow for a structured implementation (IDEs, version control, unit testing, documentation)
  

Lernziel:
Organization and Goals

Each (group of) student(s) will work on a project from the list. Suggestions for alternative problems are welcome. The outcome of the project should be as follows

1. An implemtation that solves the problem
   
2. A writtem report containing
   


• a brief description of the problem
  
• a documentation of the implementation and
  
• one or two numerical examples
  


3. a short talk about the project of max. 15 minutes plus 5 minutes of discussion in the end of the semester
   
4. each group's presentation will be evaluated by another group or student in a mini report. This way the students shall learn how to critically (and diplomatically) judge other people's work
   

• An brief overview of the projects and numerical methods
  
• An overview of suitable programming languages
  
• Maybe a little introduction to a relatively new programming language for scientific computing -- Julia -- and a good C++ library.
  
• Version control with git
  
• A few words about documentation, unit testing, debugging (verification and validation) and visualization
  

Modulkürzel:
Ma-M-S_n