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

Victorita Dolean Maini, Stephane Lanteri, Ronan Perrussel

Research output: Contribution to journalArticle

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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.
Original languageEnglish
Pages (from-to)2044-2072
Number of pages29
JournalJournal of Computational Physics
Volume227
Issue number3
DOIs
Publication statusPublished - 10 Jan 2008

Fingerprint

Domain decomposition methods
Galerkin method
Discontinuous Galerkin Method
Domain Decomposition Method
Maxwell equations
Galerkin methods
Maxwell's equations
Maxwell equation
Harmonic
Domain Decomposition
harmonics
decomposition
Three-dimensional
Decomposition
Tetrahedral Mesh
Unstructured Mesh
continuity
mesh
Discretization
Geometry

Keywords

  • computational electromagnetism
  • time-harmonic Maxwell's equations
  • discontinuous Galerkin method

Cite this

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A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods. / Dolean Maini, Victorita; Lanteri, Stephane; Perrussel, Ronan.

In: Journal of Computational Physics, Vol. 227, No. 3, 10.01.2008, p. 2044-2072.

Research output: Contribution to journalArticle

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AB - 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.

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KW - time-harmonic Maxwell's equations

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