After successful completion of the course, students are able to solve large sparse linear and non-linear systems of equations efficiently.

The students understand the various methods, know how to analyze them and how to implement the methods efficiently.

The course will cover some of the most important techniques for solving iteratively large linear systems of equations. In the first part of the lecture course, rather general methodologies such as the CG- and the GMRES methods will be discussed. The second part of the course will focus on more special methods such as multigrid and domain decomposition methods. These latter methodologies are among the most powerful tools to solve very large systems arising from the discretization of elliptic partial differential equations (e.g., by the FEM). Multigrid, for example, has optimal complexity, i.e., its cost grows linearly with the problem size.

Blackboard presentations

This lecture is part of the AKNUM elective courses.

Oral exam