Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity

Victorita Dolean; Mohamed El Bouajaji; Martin J. Gander; Stéphane Lanteri

doi:10.1007/978-3-642-11304-8_30

Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity

Victorita Dolean^*, Mohamed El Bouajaji, Martin J. Gander, Stéphane Lanteri

^*Corresponding author for this work

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

7 Citations (Scopus)

Abstract

The study of optimized Schwarz methods for Maxwell's equations started with the Helmholtz equation, see [2-4, 11]. For the rot-rot formulation of Maxwell's equations, optimized Schwarz methods were developed in [1], and for the more general form in [9, 10]. An entire hierarchy of families of optimized Schwarz methods was analyzed in [8], see also [5] for discontinuous Galerkin discretizations and large scale experiments. We present in this paper a first analysis of optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. This is an important case for real applications, and requires a new, and fundamentally different optimization of the transmission conditions. We illustrate our analysis with numerical experiments.

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XIX
Editors	Yunqing Huang, Ralf Kornhuber, Olof Widlund, Jinchao Xu
Place of Publication	London
Publisher	Springer
Pages	269-276
Number of pages	8
ISBN (Print)	9783642113031
DOIs	https://doi.org/10.1007/978-3-642-11304-8_30
Publication status	Published - 29 Oct 2010
Event	19th International Conference on Domain Decomposition, DD19 - Zhanjiajie, China Duration: 17 Aug 2009 → 22 Aug 2009

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	78
ISSN (Print)	1439-7358

Conference

Conference	19th International Conference on Domain Decomposition, DD19
Country/Territory	China
City	Zhanjiajie
Period	17/08/09 → 22/08/09

Keywords

discontinuous Galerkin
discontinuous Galerkin method
domain decomposition method
convergence factor
applied current density

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10.1007/978-3-642-11304-8_30

Cite this

Dolean, V., Bouajaji, M. E., Gander, M. J., & Lanteri, S. (2010). Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. In Y. Huang, R. Kornhuber, O. Widlund, & J. Xu (Eds.), Domain Decomposition Methods in Science and Engineering XIX (pp. 269-276). (Lecture Notes in Computational Science and Engineering; Vol. 78). Springer. https://doi.org/10.1007/978-3-642-11304-8_30

Dolean, Victorita ; Bouajaji, Mohamed El ; Gander, Martin J. et al. / Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. Domain Decomposition Methods in Science and Engineering XIX. editor / Yunqing Huang ; Ralf Kornhuber ; Olof Widlund ; Jinchao Xu. London : Springer, 2010. pp. 269-276 (Lecture Notes in Computational Science and Engineering).

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title = "Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity",

abstract = "The study of optimized Schwarz methods for Maxwell's equations started with the Helmholtz equation, see [2-4, 11]. For the rot-rot formulation of Maxwell's equations, optimized Schwarz methods were developed in [1], and for the more general form in [9, 10]. An entire hierarchy of families of optimized Schwarz methods was analyzed in [8], see also [5] for discontinuous Galerkin discretizations and large scale experiments. We present in this paper a first analysis of optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. This is an important case for real applications, and requires a new, and fundamentally different optimization of the transmission conditions. We illustrate our analysis with numerical experiments.",

keywords = "discontinuous Galerkin, discontinuous Galerkin method, domain decomposition method, convergence factor, applied current density",

author = "Victorita Dolean and Bouajaji, {Mohamed El} and Gander, {Martin J.} and St{\'e}phane Lanteri",

year = "2010",

month = oct,

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doi = "10.1007/978-3-642-11304-8_30",

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series = "Lecture Notes in Computational Science and Engineering",

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editor = "Yunqing Huang and Ralf Kornhuber and Olof Widlund and Jinchao Xu",

booktitle = "Domain Decomposition Methods in Science and Engineering XIX",

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Dolean, V, Bouajaji, ME, Gander, MJ & Lanteri, S 2010, Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. 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. 269-276, 19th International Conference on Domain Decomposition, DD19, Zhanjiajie, China, 17/08/09. https://doi.org/10.1007/978-3-642-11304-8_30

Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. / Dolean, Victorita; Bouajaji, Mohamed El; Gander, Martin J. et al.
Domain Decomposition Methods in Science and Engineering XIX. ed. / Yunqing Huang; Ralf Kornhuber; Olof Widlund; Jinchao Xu. London: Springer, 2010. p. 269-276 (Lecture Notes in Computational Science and Engineering; Vol. 78).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity

AU - Dolean, Victorita

AU - Bouajaji, Mohamed El

AU - Gander, Martin J.

AU - Lanteri, Stéphane

PY - 2010/10/29

Y1 - 2010/10/29

N2 - The study of optimized Schwarz methods for Maxwell's equations started with the Helmholtz equation, see [2-4, 11]. For the rot-rot formulation of Maxwell's equations, optimized Schwarz methods were developed in [1], and for the more general form in [9, 10]. An entire hierarchy of families of optimized Schwarz methods was analyzed in [8], see also [5] for discontinuous Galerkin discretizations and large scale experiments. We present in this paper a first analysis of optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. This is an important case for real applications, and requires a new, and fundamentally different optimization of the transmission conditions. We illustrate our analysis with numerical experiments.

AB - The study of optimized Schwarz methods for Maxwell's equations started with the Helmholtz equation, see [2-4, 11]. For the rot-rot formulation of Maxwell's equations, optimized Schwarz methods were developed in [1], and for the more general form in [9, 10]. An entire hierarchy of families of optimized Schwarz methods was analyzed in [8], see also [5] for discontinuous Galerkin discretizations and large scale experiments. We present in this paper a first analysis of optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. This is an important case for real applications, and requires a new, and fundamentally different optimization of the transmission conditions. We illustrate our analysis with numerical experiments.

KW - discontinuous Galerkin

KW - discontinuous Galerkin method

KW - domain decomposition method

KW - convergence factor

KW - applied current density

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BT - Domain Decomposition Methods in Science and Engineering XIX

A2 - Huang, Yunqing

A2 - Kornhuber, Ralf

A2 - Widlund, Olof

A2 - Xu, Jinchao

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T2 - 19th International Conference on Domain Decomposition, DD19

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Dolean V, Bouajaji ME, Gander MJ, Lanteri S. Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. In Huang Y, Kornhuber R, Widlund O, Xu J, editors, Domain Decomposition Methods in Science and Engineering XIX. London: Springer. 2010. p. 269-276. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-642-11304-8_30

Optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity

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