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Fast Solvers - Schwarz Methods, Domain Decomposition, and FETI

lecture + tutorial

by Clemens Pechstein

lecture: Thursday, 13:45 - 15:15, room T 212 (except for March 3: HS 11)

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.