Restricted Overlapping Balancing Domain Decomposition Methods and Restricted Coarse Problems for the Helmholtz Problem
Marcus Sarkis | Kimn , Jung-Han
Schwarz preconditioner | domain decomposition | coarse spaces | balancing | partition of unity | Sommerfeld interface condition | restricted additive Schwarz method | elliptic equations | finite elements | Helmholtz equation
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.