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

Document Type

Article

Publication Date

12-1-2017

Abstract

We present Nyström discretizations of multitrace/singletrace 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 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.

Identifier

85028994074 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1016/j.jcp.2017.08.050

e-ISSN

10902716

ISSN

00219991

First Page

343

Last Page

360

Volume

350

Grant

1312169

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS