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Modern Solvers for Helmholtz Problems pp 189–213Cite as

Birkhäuser

Optimized Schwarz Domain Decomposition Methods for Scalar and Vector Helmholtz Equations

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Part of the book series: Geosystems Mathematics ((GSMA))

Abstract

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.

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Acknowledgements

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 n∘2. 5020. 11, and the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles, funded by the Walloon Region under grant n∘1117545.

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Authors and Affiliations

  1. Institut Elie Cartan de Lorraine, Université de Lorraine, Inria Nancy-Grand Est EPI SPHINX, F-54506, Vandoeuvre-lès-Nancy Cedex, France

    X. Antoine

  2. Institut Montefiore B28, Université de Liège, B-4000, Liège, Belgium

    C. Geuzaine

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  1. X. Antoine
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Correspondence to C. Geuzaine .

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Editors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Domenico Lahaye

  2. Delft Institute of Applied Mathematics, Delft University of Technology VORtech B.V., Delft, The Netherlands

    Jok Tang

  3. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

    Kees Vuik

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Antoine, X., Geuzaine, C. (2017). Optimized Schwarz Domain Decomposition Methods for Scalar and Vector Helmholtz Equations. In: Lahaye, D., Tang, J., Vuik, K. (eds) Modern Solvers for Helmholtz Problems. Geosystems Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-28832-1_8

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