Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains

Victorita Dolean, Mohamed El Bouajaji, Martin J. Gander, Stéphane Lanteri, Ronan Perrussel

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

8 Citations (Scopus)

Abstract

We are interested here in the numerical modeling of time-harmonic electromagnetic wave propagation problems in irregularly shaped domains and heterogeneous media. In this context, we are naturally led to consider volume discretization methods (i.e. finite element method) as opposed to surface discretization methods (i.e. boundary element method). Most of the related existing work deals with the second order form of the time-harmonic Maxwell equations discretized by a conforming finite element method [14]. More recently, discontinuous Galerkin (DG) methods have also been considered for this purpose. While the DG method keeps almost all the advantages of a conforming finite element method (large spectrum of applications, complex geometries, etc.), the DG method has other nice properties which explain the renewed interest it gains in various domains in scientific computing: easy extension to higher order interpolation (one may increase the degree of the polynomials in the whole mesh as easily as for spectral methods and this can also be done locally), no global mass matrix to invert when solving time-domain systems of partial differential equations using an explicit time discretization scheme, easy handling of complex meshes (the mesh may be a classical conforming finite element mesh, a non-conforming one or even a mesh made of various types of elements), natural treatment of discontinuous solutions and coefficient heterogeneities and nice parallelization properties.

LanguageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XIX
EditorsYunqing Huang, Ralf Kornhuber, Olof Widlund, Jinchao Xu
Place of PublicationLondon
PublisherSpringer
Pages15-26
Number of pages12
ISBN (Print)9783642113031
DOIs
Publication statusPublished - 29 Oct 2010
Event19th International Conference on Domain Decomposition, DD19 - Zhanjiajie, China
Duration: 17 Aug 200922 Aug 2009

Publication series

NameLecture Notes in Computational Science and Engineering
Volume78
ISSN (Print)1439-7358

Conference

Conference19th International Conference on Domain Decomposition, DD19
CountryChina
CityZhanjiajie
Period17/08/0922/08/09

Fingerprint

Electromagnetic wave propagation
Domain decomposition methods
Heterogeneous Media
Domain Decomposition Method
Galerkin methods
Electromagnetic Wave
Wave Propagation
Mesh
Discontinuous Galerkin Method
Finite element method
Discretization Method
Finite Element Method
Natural sciences computing
Maxwell equations
Boundary element method
Harmonic
Partial differential equations
Interpolation
Discontinuous Solutions
Polynomials

Keywords

  • discontinuous Galerkin
  • discontinuous Galerkin method
  • domain decomposition method
  • Maxwell system
  • Schwarz method

Cite this

Dolean, V., Bouajaji, M. E., Gander, M. J., Lanteri, S., & Perrussel, R. (2010). Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains. In Y. Huang, R. Kornhuber, O. Widlund, & J. Xu (Eds.), Domain Decomposition Methods in Science and Engineering XIX (pp. 15-26). (Lecture Notes in Computational Science and Engineering; Vol. 78). London: Springer. https://doi.org/10.1007/978-3-642-11304-8_2
Dolean, Victorita ; Bouajaji, Mohamed El ; Gander, Martin J. ; Lanteri, Stéphane ; Perrussel, Ronan. / Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains. Domain Decomposition Methods in Science and Engineering XIX. editor / Yunqing Huang ; Ralf Kornhuber ; Olof Widlund ; Jinchao Xu. London : Springer, 2010. pp. 15-26 (Lecture Notes in Computational Science and Engineering).
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Dolean, V, Bouajaji, ME, Gander, MJ, Lanteri, S & Perrussel, R 2010, Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains. in Y Huang, R Kornhuber, O Widlund & J Xu (eds), Domain Decomposition Methods in Science and Engineering XIX. Lecture Notes in Computational Science and Engineering, vol. 78, Springer, London, pp. 15-26, 19th International Conference on Domain Decomposition, DD19, Zhanjiajie, China, 17/08/09. https://doi.org/10.1007/978-3-642-11304-8_2

Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains. / Dolean, Victorita; Bouajaji, Mohamed El; Gander, Martin J.; Lanteri, Stéphane; Perrussel, Ronan.

Domain Decomposition Methods in Science and Engineering XIX. ed. / Yunqing Huang; Ralf Kornhuber; Olof Widlund; Jinchao Xu. London : Springer, 2010. p. 15-26 (Lecture Notes in Computational Science and Engineering; Vol. 78).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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AU - Bouajaji, Mohamed El

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AU - Perrussel, Ronan

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AB - We are interested here in the numerical modeling of time-harmonic electromagnetic wave propagation problems in irregularly shaped domains and heterogeneous media. In this context, we are naturally led to consider volume discretization methods (i.e. finite element method) as opposed to surface discretization methods (i.e. boundary element method). Most of the related existing work deals with the second order form of the time-harmonic Maxwell equations discretized by a conforming finite element method [14]. More recently, discontinuous Galerkin (DG) methods have also been considered for this purpose. While the DG method keeps almost all the advantages of a conforming finite element method (large spectrum of applications, complex geometries, etc.), the DG method has other nice properties which explain the renewed interest it gains in various domains in scientific computing: easy extension to higher order interpolation (one may increase the degree of the polynomials in the whole mesh as easily as for spectral methods and this can also be done locally), no global mass matrix to invert when solving time-domain systems of partial differential equations using an explicit time discretization scheme, easy handling of complex meshes (the mesh may be a classical conforming finite element mesh, a non-conforming one or even a mesh made of various types of elements), natural treatment of discontinuous solutions and coefficient heterogeneities and nice parallelization properties.

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Dolean V, Bouajaji ME, Gander MJ, Lanteri S, Perrussel R. Domain decomposition methods for electromagnetic wave propagation problems in heterogeneous media and complex domains. In Huang Y, Kornhuber R, Widlund O, Xu J, editors, Domain Decomposition Methods in Science and Engineering XIX. London: Springer. 2010. p. 15-26. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-11304-8_2