A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods

Authors:
Victorita Dolean;Stéphane Lanteri;Ronan Perrussel
Affiliations:
INRIA, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France and Université de Nice-Sophia Antipolis, Laboratoire J.A. Dieudonné, CNRS UMR 6621, 06108 Nice Cedex, France;INRIA, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France;Laboratoire Ampère, CNRS UMR 5005, Universíté de Lyon, Ecole Centrale de Lyon, 69134 ícully Cedex, France
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

We present here a domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by a discontinuous Galerkin method. In order to allow the treatment of irregularly shaped geometries, the discontinuous Galerkin method is formulated on unstructured tetrahedral meshes. The domain decomposition strategy takes the form of a Schwarz-type algorithm where a continuity condition on the incoming characteristic variables is imposed at the interfaces between neighboring subdomains. A multifrontal sparse direct solver is used at the subdomain level. The resulting domain decomposition strategy can be viewed as a hybrid iterative/direct solution method for the large, sparse and complex coefficients algebraic system resulting from the discretization of the time-harmonic Maxwell equations by a discontinuous Galerkin method.