Methods and Algorithms for Scientific Computing

Optimized Schwarz Methods with Overlap for the Helmholtz Equation

Abstract

Optimized Schwarz methods are based on optimized transmission conditions between subdomains and can have substantially improved convergence behavior compared to classical Schwarz methods. This is especially true when the method is applied to the Helmholtz equation, and better transmission conditions in the form of perfectly matched layers have, for example, led to the new class of sweeping preconditioners. We present here for the first time a complete analysis of optimized Schwarz methods with overlap for the Helmholtz equation. We obtain closed form asymptotically optimized transmission conditions for the case of two subdomains and study numerically the influence of the number of subdomains on this optimized choice.

Keywords

  1. overlapping optimized Schwarz methods
  2. Helmholtz equation

MSC codes

  1. 65N55
  2. 65N22
  3. 65F10

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A3195 - A3219
ISSN (online): 1095-7197

History

Submitted: 15 May 2015
Accepted: 1 August 2016
Published online: 6 October 2016

Keywords

  1. overlapping optimized Schwarz methods
  2. Helmholtz equation

MSC codes

  1. 65N55
  2. 65N22
  3. 65F10

Authors

Affiliations

Funding Information

Zhejiang Ocean University: Research Start Funding
National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809: 11371287

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