Convergence of classical optimized non-overlapping Schwarz method for Helmholtz problems in closed domains

Abstract

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 0 th -order, evanescent modes damping, optimized 2 nd -order and Padé-localized square-root transmission conditions will be discussed.

Solution of time-harmonic Maxwell's equations by a domain decomposition method based on PML transmission conditions

“…However, since the cost of computing the exact DtN is prohibitive, low-order absorbing boundary conditions (ABCs) to approximate the DtN have been developed. Nonetheless, these methods have limited accuracy, which led to developing domain decomposition strategies with high order transmission conditions [10]. But the problem with high order transmission conditions is the difficulty of their implementation.…”