Schur complement Domain Decomposition Methods for the solution of multiple scattering problems

Pedneault, Michael; Turc, Catalin; Boubendir, Yassine

doi:10.48550/arxiv.1608.00034

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“…The first approach consist of hierarchical elimination from the DDM linear system via Schur complements of the Robin data corresponding to interior subdomain interfaces. This idea was presented recently as a hierarchical merging of Robin-to-Robin (RtR) maps [17] in the context of scattering from variable media with smooth index of refraction, and was shown to be equivalent to hierarchical elimination of interior Robin data from the DDM linear system corresponding to multiple scattering [28]. The advantage of the Schur complement DDM is that at each stage inverses of relatively small matrices need be computed, and these can be performed in a hierarchical fashion that optimizes the computational cost without compromising the inherent parallelism of DDM.…”

Section: Introductionmentioning

confidence: 99%

Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

Jerez-Hanckes

Pérez‐Arancibia

Turc

2017

Journal of Computational Physics

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We present Nyström discretizations of multitrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and generalized Robin boundary conditions. The generalized Robin boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the classical version of DDM is not particularly well suited for Krylov subspace iterative solvers, we show that the associated DDM linear system can be efficiently solved by hierarchical elimination via Schur complements of the Robin data. We show through numerical examples that the latter version of DDM gives rise to small numbers of Krylov subspace iterations that depend mildly on the frequency and number of subdomains.

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Section: Introductionmentioning

confidence: 99%