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Domain Decomposition Methods based on quasi-optimal transmission operators for the solution of Helmholtz transmission problems. (arXiv:1710.02694v1 [math.NA])
来源于:arXiv
We present non-overlapping Domain Decomposition Methods (DDM) based on
quasi-optimal transmission operators for the solution of Helmholtz transmission
problems with piece-wise constant material properties. The quasi-optimal
transmission boundary conditions incorporate readily available approximations
of Dirichlet-to-Neumann operators. These approximations consist of either
complexified hypersingular boundary integral operators for the Helmholtz
equation or square root Fourier multipliers with complex wavenumbers. We show
that under certain regularity assumptions on the closed interface of material
discontinuity, the DDM with quasi-optimal transmission conditions are
well-posed. We present a DDM framework based on Robin-to-Robin (RtR) operators
that can be computed robustly via boundary integral formulations. More
importantly, the use of quasi-optimal transmission operators results in DDM
that converge in small numbers of iterations even in the challenging
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