Restricted overlapping balancing domain decomposition methods and restricted coarse problems for the Helmholtz problem |
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Authors: | Jung-Han Kimn Marcus Sarkis |
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Affiliation: | a Department of Mathematics, The Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA b Mathematical Sciences Department, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA c Instituto de Matemática Pura e Aplicada, Est. Dona Castorina, 110, Rio de Janeiro, RJ, CEP 22420-320, Brazil |
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Abstract: | 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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Keywords: | Schwarz preconditioner Domain decomposition Coarse spaces Balancing Partition of unity Sommerfeld interface condition Restricted additive Schwarz method Elliptic equations Finite elements Helmholtz equation |
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