The Optimized Schwarz Method with a Coarse Grid Correction

Authors:
Olivier Dubois;Martin J. Gander;Sébastien Loisel;Amik St-Cyr;Daniel B. Szyld
Affiliations:
dubois@ima.umn.edu;martin.gander@unige.ch;S.Loisel@hw.ac.uk;amik.st-cyr@shell.com;szyld@temple.edu
Venue:
SIAM Journal on Scientific Computing
Year:
2012

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Abstract

Optimized Schwarz methods (OSMs) use Robin transmission conditions across the subdomain interfaces. The Robin parameter can then be optimized to obtain the fastest convergence. A new formulation is presented with a coarse grid correction. The optimal parameter is computed for a model problem on a cylinder, together with the corresponding convergence factor which is smaller than that of classical Schwarz methods. A new coarse space is presented, suitable for OSM. Numerical experiments illustrating the effectiveness of OSM with a coarse grid correction, both as an iteration and as a preconditioner, are reported.