Edited by: F. Magoulès

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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