Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations

Victorita Dolean; Martin J. Gander; Erwin Veneros; Hui Zhang

doi:10.1007/978-3-319-52389-7_13

Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations

Victorita Dolean, Martin J. Gander, Erwin Veneros, Hui Zhang

Mathematics And Statistics

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

1 Citation (Scopus)

Abstract

Both the Helmholtz equation and the time-harmonic Maxwell’s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most promising techniques for this task. We focus here on the case of dissipative and conductive media with strongly heterogeneous coefficients, and develop optimized transmission conditions for this case. We establish a link for the use of such conditions between the case of Helmholtz and Maxwell’s equations, and show that in both cases jumps aligned with the interfaces of the subdomains can improve the convergence of the subdomain iteration.

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XXIII
Place of Publication	Berlin
Publisher	Springer-Verlag
Pages	145-152
Number of pages	8
ISBN (Print)	9783319523880, 9783319523897
DOIs	https://doi.org/10.1007/978-3-319-52389-7_13
Publication status	Published - 18 Mar 2017
Event	23rd International Conference on Domain Decomposition Methods, DD23 - Jeju Island, Korea, Republic of Duration: 6 Jul 2015 → 10 Jul 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	116
ISSN (Print)	1439-7358

Conference

Conference	23rd International Conference on Domain Decomposition Methods, DD23
Country	Korea, Republic of
City	Jeju Island
Period	6/07/15 → 10/07/15

Keywords

discontinuous coefficients
Helmholtz equation
Maxwell’s equations
optimized Schwarz methods

Access to Document

10.1007/978-3-319-52389-7_13

Dolean-etal-2017-Optimized-Schwarz-methods-for-heterogeneous-Helmholtz-and-Maxwells-equationsAccepted author manuscript, 119 KB

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Cite this

Dolean, V., Gander, M. J., Veneros, E., & Zhang, H. (2017). Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations. In Domain Decomposition Methods in Science and Engineering XXIII (pp. 145-152). (Lecture Notes in Computational Science and Engineering; Vol. 116). Springer-Verlag. https://doi.org/10.1007/978-3-319-52389-7_13

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abstract = "Both the Helmholtz equation and the time-harmonic Maxwell{\textquoteright}s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most promising techniques for this task. We focus here on the case of dissipative and conductive media with strongly heterogeneous coefficients, and develop optimized transmission conditions for this case. We establish a link for the use of such conditions between the case of Helmholtz and Maxwell{\textquoteright}s equations, and show that in both cases jumps aligned with the interfaces of the subdomains can improve the convergence of the subdomain iteration.",

keywords = "discontinuous coefficients, Helmholtz equation, Maxwell{\textquoteright}s equations , optimized Schwarz methods",

author = "Victorita Dolean and Gander, {Martin J.} and Erwin Veneros and Hui Zhang",

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Dolean, V, Gander, MJ, Veneros, E & Zhang, H 2017, Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations. in Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol. 116, Springer-Verlag, Berlin, pp. 145-152, 23rd International Conference on Domain Decomposition Methods, DD23, Jeju Island, Korea, Republic of, 6/07/15. https://doi.org/10.1007/978-3-319-52389-7_13

Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell's equations. / Dolean, Victorita; Gander, Martin J.; Veneros, Erwin; Zhang, Hui.

Domain Decomposition Methods in Science and Engineering XXIII. Berlin : Springer-Verlag, 2017. p. 145-152 (Lecture Notes in Computational Science and Engineering; Vol. 116).

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

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AU - Gander, Martin J.

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AU - Zhang, Hui

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Y1 - 2017/3/18

N2 - Both the Helmholtz equation and the time-harmonic Maxwell’s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most promising techniques for this task. We focus here on the case of dissipative and conductive media with strongly heterogeneous coefficients, and develop optimized transmission conditions for this case. We establish a link for the use of such conditions between the case of Helmholtz and Maxwell’s equations, and show that in both cases jumps aligned with the interfaces of the subdomains can improve the convergence of the subdomain iteration.

AB - Both the Helmholtz equation and the time-harmonic Maxwell’s equations are difficult to solve by iterative methods in the intermediate to high frequency regime, and domain decomposition methods are among the most promising techniques for this task. We focus here on the case of dissipative and conductive media with strongly heterogeneous coefficients, and develop optimized transmission conditions for this case. We establish a link for the use of such conditions between the case of Helmholtz and Maxwell’s equations, and show that in both cases jumps aligned with the interfaces of the subdomains can improve the convergence of the subdomain iteration.

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KW - Maxwell’s equations

KW - optimized Schwarz methods

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