Optimized schwarz methods for Maxwell equations with discontinuous coefficients

Victorita Dolean, Martin J. Gander, Erwin Veneros

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

2 Citations (Scopus)

Abstract

We study non-overlapping Schwarz methods for solving time-harmonic Maxwell’s equations in heterogeneous media. We show that the classical Schwarz algorithm is always divergent when coefficient jumps are present along the interface. In the case of transverse magnetic or transverse electric two dimensional formulations, convergence can be achieved in specific configurations only. We then develop optimized Schwarz methods which can take coefficient jumps into account in their transmission conditions. These methods exhibit rapid convergence, and sometimes converge independently of the mesh parameter, even without overlap. We illustrate our analysis with numerical experiments.
Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXI
EditorsJocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund
Place of PublicationBerlin
PublisherSpringer
Pages517-525
Number of pages9
ISBN (Electronic)9783319057880, 9783319057897
DOIs
Publication statusPublished - 14 Nov 2014
Event21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014 - Rennes, France
Duration: 25 Jun 201229 Jun 2012

Publication series

NameLecture Notes in Computational Science and Engineering
Volume98
ISSN (Print)1439-7358

Conference

Conference21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014
CountryFrance
CityRennes
Period25/06/1229/06/12

Fingerprint

Schwarz Methods
Discontinuous Coefficients
Maxwell equations
Maxwell's equations
Jump
Transverse
Transmission Conditions
Heterogeneous Media
Coefficient
Overlap
Harmonic
Experiments
Numerical Experiment
Mesh
Converge
Configuration
Formulation

Keywords

  • transverse electric
  • transmission condition
  • convergence factor
  • applied current density
  • mesh parameter

Cite this

Dolean, V., Gander, M. J., & Veneros, E. (2014). Optimized schwarz methods for Maxwell equations with discontinuous coefficients. In J. Erhel, M. J. Gander, L. Halpern, G. Pichot, T. Sassi, & O. Widlund (Eds.), Domain Decomposition Methods in Science and Engineering XXI (pp. 517-525). (Lecture Notes in Computational Science and Engineering; Vol. 98). Berlin: Springer. https://doi.org/10.1007/978-3-319-05789-7_49
Dolean, Victorita ; Gander, Martin J. ; Veneros, Erwin. / Optimized schwarz methods for Maxwell equations with discontinuous coefficients. Domain Decomposition Methods in Science and Engineering XXI. editor / Jocelyne Erhel ; Martin J. Gander ; Laurence Halpern ; Géraldine Pichot ; Taoufik Sassi ; Olof Widlund. Berlin : Springer, 2014. pp. 517-525 (Lecture Notes in Computational Science and Engineering).
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abstract = "We study non-overlapping Schwarz methods for solving time-harmonic Maxwell’s equations in heterogeneous media. We show that the classical Schwarz algorithm is always divergent when coefficient jumps are present along the interface. In the case of transverse magnetic or transverse electric two dimensional formulations, convergence can be achieved in specific configurations only. We then develop optimized Schwarz methods which can take coefficient jumps into account in their transmission conditions. These methods exhibit rapid convergence, and sometimes converge independently of the mesh parameter, even without overlap. We illustrate our analysis with numerical experiments.",
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Dolean, V, Gander, MJ & Veneros, E 2014, Optimized schwarz methods for Maxwell equations with discontinuous coefficients. in J Erhel, MJ Gander, L Halpern, G Pichot, T Sassi & O Widlund (eds), Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol. 98, Springer, Berlin, pp. 517-525, 21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014, Rennes, France, 25/06/12. https://doi.org/10.1007/978-3-319-05789-7_49

Optimized schwarz methods for Maxwell equations with discontinuous coefficients. / Dolean, Victorita; Gander, Martin J.; Veneros, Erwin.

Domain Decomposition Methods in Science and Engineering XXI. ed. / Jocelyne Erhel; Martin J. Gander; Laurence Halpern; Géraldine Pichot; Taoufik Sassi; Olof Widlund. Berlin : Springer, 2014. p. 517-525 (Lecture Notes in Computational Science and Engineering; Vol. 98).

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

TY - GEN

T1 - Optimized schwarz methods for Maxwell equations with discontinuous coefficients

AU - Dolean, Victorita

AU - Gander, Martin J.

AU - Veneros, Erwin

PY - 2014/11/14

Y1 - 2014/11/14

N2 - We study non-overlapping Schwarz methods for solving time-harmonic Maxwell’s equations in heterogeneous media. We show that the classical Schwarz algorithm is always divergent when coefficient jumps are present along the interface. In the case of transverse magnetic or transverse electric two dimensional formulations, convergence can be achieved in specific configurations only. We then develop optimized Schwarz methods which can take coefficient jumps into account in their transmission conditions. These methods exhibit rapid convergence, and sometimes converge independently of the mesh parameter, even without overlap. We illustrate our analysis with numerical experiments.

AB - We study non-overlapping Schwarz methods for solving time-harmonic Maxwell’s equations in heterogeneous media. We show that the classical Schwarz algorithm is always divergent when coefficient jumps are present along the interface. In the case of transverse magnetic or transverse electric two dimensional formulations, convergence can be achieved in specific configurations only. We then develop optimized Schwarz methods which can take coefficient jumps into account in their transmission conditions. These methods exhibit rapid convergence, and sometimes converge independently of the mesh parameter, even without overlap. We illustrate our analysis with numerical experiments.

KW - transverse electric

KW - transmission condition

KW - convergence factor

KW - applied current density

KW - mesh parameter

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BT - Domain Decomposition Methods in Science and Engineering XXI

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Dolean V, Gander MJ, Veneros E. Optimized schwarz methods for Maxwell equations with discontinuous coefficients. In Erhel J, Gander MJ, Halpern L, Pichot G, Sassi T, Widlund O, editors, Domain Decomposition Methods in Science and Engineering XXI. Berlin: Springer. 2014. p. 517-525. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-05789-7_49