Convergence of optimized non-overlapping Schwarz method for Helmholtz problems in closed domains
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In this paper we discuss the convergence of state-of-the-art optimized Schwarz transmission conditions for Helmholtz problems defined on closed domains (i.e. setups which do not exhibit an outgoing wave condition), as commonly encountered when modeling cavities. In particular, the impact of back-propagating waves on the Dirichlet-to-Neumann map will be analyzed. Afterwards, the performance of the well-established optimized 0th-order, evanescent modes damping, optimized 2nd-order and Padé-localized square-root transmission conditions will be discussed.
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