Optimized Schwarz Domain Decomposition Methods for Scalar and Vector Helmholtz Equations

  • X. Antoine
  • C. GeuzaineEmail author
Part of the Geosystems Mathematics book series (GSMA)


In this chapter we review Schwarz domain decomposition methods for scalar and vector Helmholtz equations, with a focus on the choice of the associated transmission conditions between the subdomains. The methods are analyzed in both acoustic and electromagnetic settings, and generic weak formulations directly amenable to finite element discretization are presented. An open source solver along with ready-to-use examples is freely available online for further testing.


Domain Decomposition Transmission Condition Perfectly Match Layer Domain Decomposition Method Transmission Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by the Wallonia-Brussels Federation (ARC grant for Concerted Research Actions ARC WAVES 15/19-03), the Belgian Science Policy (PAI grant P7/02), the Walloon Region (WIST3 grants ONELAB and ALIZEES), the French ANR (grant MicroWave NT09 460489 “Programme Blanc”) and the “EADS Foundation” (High-BRID project, grant 089-1009-1006). Computational resources have been provided by CÉCI, funded by F.R.S.-FNRS (Fonds de la Recherche Scientifique) under grant n2. 5020. 11, and the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles, funded by the Walloon Region under grant n1117545.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut Elie Cartan de LorraineUniversité de Lorraine, Inria Nancy-Grand Est EPI SPHINXVandoeuvre-lès-Nancy CedexFrance
  2. 2.Institut Montefiore B28Université de LiègeLiègeBelgium

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