An adaptive gdsw coarse space for two-level overlapping schwarz methods in two dimensions

Book chapter (2018)

Authors

A. Heinlein University of Cologne

Axel Klawonn University of Cologne

Jascha Knepper University of Cologne

Oliver Rheinbach University of Technology Bergakademie Freiberg

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Published Date

2018

Language

English

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Abstract

We propose robust coarse spaces for two-level overlapping Schwarz preconditioners, which are extensions of the energy minimizing coarse space known as GDSW (Generalized Dryja, Smith, Widlund). The resulting two-level methods with adaptive coarse spaces are robust for second order elliptic problems in two dimensions, even in presence of a highly heterogeneous coefficient function, and reduce to the standard GDSW algorithm if no additional coarse basis functions are used.