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MESH PARTITIONING TECHNIQUES AND DOMAIN DECOMPOSITION METHODS
Edited by: F. Magoulès
Fast Schwarz Domain Decomposition Methods through Extrapolation
CERFACS, Toulouse, France
F. Hülsemann, "Fast Schwarz Domain Decomposition Methods through Extrapolation", in F. Magoulès, (Editor), "Mesh Partitioning Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 11, pp 269-292, 2007. doi:10.4203/csets.17.11
Keywords: domain decomposition, overlapping Schwarz algorithm, extrapolation, elliptic partial differential equations.
The topic of this chapter is the Aitken-Schwarz method on strip-like subdomains for separable, second order elliptic differential operators. The Aitken-Schwarz approach is essentially an extrapolation of the boundary conditions on the inter-partition interfaces. Its fast convergence property, which is backed up by numerical experiments, makes the method well suited for parallel metacomputing settings. A reformulation of the method that aims to reduce the preprocessing costs is presented and its convergence is examined in numerical experiments.
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