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Restricted overlapping balancing domain decomposition methods and restricted coarse problems for the Helmholtz problem

✍ Scribed by Jung-Han Kimn; Marcus Sarkis

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 288 KB
Volume: 196
Category: Article
ISSN: 0045-7825
DOI: 10.1016/j.cma.2006.03.016

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✦ Synopsis

Overlapping balancing domain decomposition methods and their combination with restricted additive Schwarz methods are proposed for the Helmholtz equation. These new methods also extend previous work on non-overlapping balancing domain decomposition methods toward simplifying their coarse problems and local solvers. They also extend restricted Schwarz methods, originally designed to overlapping domain decomposition and Dirichlet local solvers, to the case of non-overlapping domain decomposition and/or Neumann and Sommerfeld local solvers. Finally, we introduce coarse spaces based on partitions of unity and planes waves, and show how oblique projection coarse problems can be designed from restricted additive Schwarz methods. Numerical tests are presented.

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