In this elective course E6, designed for participants of the COMMAS master of science program, we want to build a parallel numerical solver for a typical eliptical partial differential equation from scratch and use it to solve in a case study a real world problem. For the sake of simplicity we use the groundwater flow equation and a contamination problem as example.

Topics of the lecture are:

1. Introduction to the problem and to object oriented programming
2. C++: Classes and Inheritance
3. C++: Generic Programming and the STL
4. Iterative linear solvers: Basics
5. Iterative linear solvers: Advanced methods
6. Iterative linear solvers: Multigrid
7. Flow in porous media
8. The Finite-Volume-Method
9. Grids and grid generation
10. Parallel Computers
11. Parallel Programming: MPI
12. Parallel Programming: Parallel iterative solvers
13. Time dependend problems, Solute Transport

What you will learn:

Modern programming techniques and their application to the numerical solution of partial differential equations

• Knowledge of basic programing concepts like loops, conditions and variables.
• Basic knowledge about partial differential equations (content of COMMAS C5 lecture)
• Readiness to do some programming in the exercises

• Introduction to C++-Programming
• C++-Language Tutorial
• C/C++ Reference
• Bjarne Stroustrup: The C++ Programming Language, 3rd ed., Addison-Wesley Longman, 1997.
• Nicolai M. Josuttis: The C++ Standard Library - A Tutorial and Reference, 1st ed., Addison-Wesley, 1999.
• P. Bastian: Vorlesungsskript Paralleles Rechnen I