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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:350

Article

Jerez-Hanckes, Carlos¹  Perez-Arancibia, Carlos^1,2,3  Turc, Catalin^4,5 

[1] Pontificia Univ Catolica Chile, Sch Engn, Inst Math & Computat Engn, Av Vicuna Mackenna 4860, Santiago, Chile

[2] MIT, Dept Math, Cambridge, MA 02139 USA

[3] Pontificia Univ Catolica Chile, Fac Math, Santiago, Chile

[4] New Jersey Inst Technol, Dept Math Sci, 323 Dr ML King Jr Blvd, Newark, NJ 07102 USA

[5] New Jersey Inst Technol, Ctr Appl Math & Stat, 323 Dr ML King Jr Blvd, Newark, NJ 07102 USA

关键词: Multiple junctions;    Multitrace formulations;    Single trace formulations;    Domain decomposition methods;   

DOI  :  10.1016/j.jcp.2017.08.050

来源: Elsevier

【 摘 要 】

We present Nystrom 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 Neunlann 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free