# Fast Solvers - Schwarz Methods, Domain Decomposition, and FETI

by Clemens Pechstein

tutorial: Thursday, 15:30 - 16:15, room T 212 (tutorial starts on March 10)

The efficient solution of large-scale linear systems, which stem
from the finite-element discretization of elliptic partial differential
equations, is in general a difficult problem.
The main idea of domain decomposition methods is to solve this *large* problem iteratively by solving suitable *smaller*
problems several times.
The smaller problems usually correspond to *subdomains*
into which the computational domain is decomposed.

In this lecture I would like to give an overview over leading domain decomposition methods, and we will work out the mathematics in the derivation and the convergence analysis of these methods.

- Introduction
- Theory of abstract Schwarz methods
- Two-level overlapping Schwarz methods
- Iterative substructuring methods

Lecture notes will be provided at the end of the course.
The lecture is based on parts of
A. Toselli and O. Widlund, *Domain Decomposition Methods
- Algorithms and Theory*, Springer-Verlag, Berlin, 2005.

Special information for DK-students: The major part of the course lives clearly in numerical analysis. There is a minor part dealing with algebra: algebraic identities and inequalities, projections, pseudo-inverses, etc.