Influence of perturbations in transmission conditions on the convergence of the domain decomposition method for the Helmholtz equation

Authors

  • A.F. Zaitseva
  • V.V. Lisitsa

Keywords:

domain decomposition method
Helmholtz equation
Dirichlet-to-Neumann map
finite difference method
method of small perturbations
convergence of iterative processes

Abstract

The domain decomposition is a widely used technique applied in parallel iterative solvers of the Helmholtz equation with the convergence rate controlled by the quality of transmission conditions. The optimal conditions are those based on the Dirichlet-to-Neumann map. However, if grid-based numerical methods are used to solve the Helmholtz equation, this map needs to be localized, which induces artificial grid-independent perturbations in the transmission conditions. In this paper it is proved that if the perturbations are nonsymmetric, i.e. different errors are induced in the adjoint subdomains, then the domain decomposition method converges to a solution of a problem differing from the original one. In other words, there exists an irreducible error.

New computational technologies

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Published

2014-08-11

Issue

Vol. 15 (2014): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biographies

A.F. Zaitseva

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Engineer

V.V. Lisitsa

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Head of Laboratory

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