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DIRICHLET/DIRICHLET AND DIRICHLET/DIRICHLET-NEUMANN/NEUMANN NON-OVERLAPPING ITERATIVE DOMAIN DECOMPOSITION METHODS

Abstract

A new iterative non-overlapping domain decomposition method is proposed for solving the one- and two-dimensional Helmholtz equation on parallel computers. The spectral collocation method is applied to solve the Helmholtz equation in each subdomain based on the Chebyshev approximation, while the patching conditions are imposed at the interfaces between subdomains through a correction, being a linear function of the space coordinates. Convergence analysis is performed for two applications of the proposed method (DDLC and DDNNLC algorithms – the meaning of these abbreviations is explained below) based on the works of Zanolli and Funaro et al.

Numerical tests have been performed and results obtained using the proposed method and other iterative algorithms have been compared. Parallel performance of the multi-domain algorithms has been analyzed by decomposing the two-dimensional domain into a number of subdomains in one spatial direction.

For the one–dimensional problem, convergence of the iteration process was quickly obtained using the proposed method, setting a small value of the σ constant in the Helmholtz equation. Another application of the proposed method may be an alternative to other iterative schemes when solving the two-dimensional Helmholtz equation.

Keywords:

non-overlapping domain decomposition method, parallel computing, spectral methods, Helmholtz equation

Details

Issue
Vol. 12 No. 1-2 (2008)
Section
Research article
Published
2008-06-30
Licencja:
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Author Biographies

SŁAWOMIR KUBACKI,
Czestochowa University of Technology, Institute of Thermal Machinery



ANDRZEJ BOGUSŁAWSKI,
Czestochowa University of Technology, Institute of Thermal Machinery



Authors

  • SŁAWOMIR KUBACKI

    Czestochowa University of Technology, Institute of Thermal Machinery
  • ANDRZEJ BOGUSŁAWSKI

    Czestochowa University of Technology, Institute of Thermal Machinery

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