Abstract
Several variants of Schwarz domain decomposition, which differ in the choice of interface conditions, are studied in a finite volume context. Krylov subspace acceleration, GMRES in this paper, is used to accelerate convergence. Using a detailed investigation of the systems involved, we can minimize the memory requirements of GMRES acceleration. It is shown how Krylov subspace acceleration can be easily built on top of an already implemented Schwarz domain decomposition iteration, which makes Krylov-Schwarz algorithms easy to use in practice. The convergence rate is investigated both theoretically and experimentally. It is observed that the Krylov subspace accelerated algorithm is quite insensitive to the type of interface conditions employed.
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Brakkee, E., Wilders, P. The Influence of Interface Conditions on Convergence of Krylov-Schwarz Domain Decomposition for the Advection-Diffusion Equation. Journal of Scientific Computing 12, 11–30 (1997). https://doi.org/10.1023/A:1025602319278
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DOI: https://doi.org/10.1023/A:1025602319278