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

Carlos Jerez-Hanckes, C. Pérez-Arancibia, Catalin Turc*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

We present Nyström discretizations of multitrace/singletrace formulations and nonoverlapping 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 optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative
solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute
efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM
linear system can be efficiently solved via hierarchical Schur complements elimination.
Original languageEnglish
Pages (from-to)343-360
Number of pages18
JournalJournal of computational physics
Volume350
Early online date31 Aug 2017
DOIs
Publication statusPublished - 1 Dec 2017
Externally publishedYes

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