Convergence analysis of Schwarz methods without overlap for the Helmholtz equation

F. Magoulès, P. Iványi, B. H V Topping

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


In this paper, the continuous and discrete optimal transmission conditions for the Schwarz algorithm without overlap for the Helmholtz equation are studied. Since such transmission conditions lead to non-local operators, they are approximated through two different approaches. The first approach, called optimized, consists of an approximation of the optimal continuous transmission conditions with partial differential operators, which are then optimized for efficiency. The second approach, called approximated, is based on pure algebraic operations performed on the optimal discrete transmission conditions. After demonstrating the optimal convergence properties of the Schwarz algorithm new numerical investigations are performed on a wide range of unstructured meshes and arbitrary mesh partitioning with cross points. Numerical results illustrate for the first time the effectiveness, robustness and comparative performance of the optimized and approximated Schwarz methods on a model problem and on industrial problems. © 2004 Published by Elseiver Ltd.

Original languageEnglish
Pages (from-to)1835-1847
Number of pages13
JournalComputers and Structures
Issue number22
Publication statusPublished - Sept 2004


  • Accoustics
  • Convergence analysis
  • Domain decomposition
  • Helmholtz equation
  • Schwarz method
  • Transmission conditions


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