Sweeping Preconditioners for the Iterative Solution of Quasiperiodic Helmholtz Transmission Problems in Layered Media

Document Type

Article

Publication Date

2-1-2020

Abstract

We present a sweeping preconditioner for quasi-optimal domain decomposition methods (DD) applied to Helmholtz transmission problems in periodic layered media. Quasi-optimal DD (QO DD) for Helmholtz equations rely on transmission operators that are approximations of Dirichlet-to-Neumann (DtN) operators. Employing shape perturbation series, we construct approximations of DtN operators corresponding to periodic domains, which we then use as transmission operators in a non-overlapping DD framework. The Robin-to-Robin (RtR) operators that are the building blocks of DD are expressed via robust boundary integral equation formulations. We use Nyström discretizations of quasiperiodic boundary integral operators to construct high-order approximations of RtR. Based on the premise that the quasi-optimal transmission operators should act like perfect transparent boundary conditions, we construct an approximate LU factorization of the tridiagonal QO Schwarz iteration matrix associated with periodic layered media, which is then used as a double sweep preconditioner. We present a variety of numerical results that showcase the effectiveness of the sweeping preconditioners applied to QO DD for the iterative solution of Helmholtz transmission problems in periodic layered media.

Identifier

85079319169 (Scopus)

Publication Title

Journal of Scientific Computing

External Full Text Location

https://doi.org/10.1007/s10915-020-01133-z

e-ISSN

15737691

ISSN

08857474

Issue

2

Volume

82

Grant

1522548

Fund Ref

National Science Foundation

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