Achieving robustness through coarse space enrichment in the two level Schwarz framework

Spillane, Nicole and Dolean, Victorita and Hauret, Patrice and Nataf, Frédéric and Pechstein, Clemens and Scheichl, Robert; Erhel, Jocelyne and Gander, Martin J. and Halpern, Laurence and Pichot, Géraldine and Sassi, Taoufik and Widlund, Olof, eds. (2014) Achieving robustness through coarse space enrichment in the two level Schwarz framework. In: Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, 98 . Springer-Verlag, FRA, pp. 447-456. ISBN 9783319057897 (https://doi.org/10.1007/978-3-319-05789-7_42)

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Abstract

As many DD methods the two level Additive Schwarz method may suffer from a lack of robustness with respect to coefficient variation. This is the case in particular if the partition into is not aligned with all jumps in the coefficients. The theoretical analysis traces this lack of robustness back to the so called stable splitting property. In this work we propose to solve a generalized eigenvalue problem in each subdomain which identifies which vectors are responsible for violating the stable splitting property. These vectors are used to span the coarse space and taken care of by a direct solve while all remaining components behave well. The result is a condition number estimate for the two level method which does not depend on the number of subdomains or any jumps in the coefficients.

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