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

^*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

2 Citations (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
Editors	Hyea Hyun Kim, Axel Klawonn, Eun-Jae Park, Chang-Ock Lee, Olof B. Widlund, Xiao-Chuan Cai, David E. Keyes
Publisher	Springer Verlag
Pages	145-152
Number of pages	8
ISBN (Print)	9783319523880
DOIs	https://doi.org/10.1007/978-3-319-52389-7_13
Publication status	Published - 2017
Externally published	Yes
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/Territory	Korea, Republic of
City	Jeju Island
Period	6/07/15 → 10/07/15

Access to Document

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

Cite this

Dolean, V., Gander, M. J., Veneros, E., & Zhang, H. (2017). Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell’s equations. In H. H. Kim, A. Klawonn, E.-J. Park, C.-O. Lee, O. B. Widlund, X.-C. Cai, & D. E. Keyes (Eds.), 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

Dolean, Victorita ; Gander, Martin J. ; Veneros, Erwin et al. / Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell’s equations. Domain Decomposition Methods in Science and Engineering XXIII. editor / Hyea Hyun Kim ; Axel Klawonn ; Eun-Jae Park ; Chang-Ock Lee ; Olof B. Widlund ; Xiao-Chuan Cai ; David E. Keyes. Springer Verlag, 2017. pp. 145-152 (Lecture Notes in Computational Science and Engineering).

@inproceedings{aa85269ce01544a3bdb40c333fcb1350,

title = "Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell{\textquoteright}s equations",

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.",

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

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.; 23rd International Conference on Domain Decomposition Methods, DD23 ; Conference date: 06-07-2015 Through 10-07-2015",

year = "2017",

doi = "10.1007/978-3-319-52389-7_13",

language = "English",

isbn = "9783319523880",

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

publisher = "Springer Verlag",

pages = "145--152",

editor = "Kim, {Hyea Hyun} and Axel Klawonn and Eun-Jae Park and Chang-Ock Lee and Widlund, {Olof B.} and Xiao-Chuan Cai and Keyes, {David E.}",

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

}

Dolean, V, Gander, MJ, Veneros, E & Zhang, H 2017, Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell’s equations. in HH Kim, A Klawonn, E-J Park, C-O Lee, OB Widlund, X-C Cai & DE Keyes (eds), Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol. 116, Springer Verlag, 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 et al.
Domain Decomposition Methods in Science and Engineering XXIII. ed. / Hyea Hyun Kim; Axel Klawonn; Eun-Jae Park; Chang-Ock Lee; Olof B. Widlund; Xiao-Chuan Cai; David E. Keyes. Springer Verlag, 2017. p. 145-152 (Lecture Notes in Computational Science and Engineering; Vol. 116).

Research output: Chapter in Book or Report/Conference proceeding › Conference Proceeding › peer-review

TY - GEN

T1 - Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell’s equations

AU - Dolean, Victorita

AU - Gander, Martin J.

AU - Veneros, Erwin

AU - Zhang, Hui

N1 - Publisher Copyright: © Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

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.

UR - http://www.scopus.com/inward/record.url?scp=85016219310&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-52389-7_13

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

M3 - Conference Proceeding

AN - SCOPUS:85016219310

SN - 9783319523880

T3 - Lecture Notes in Computational Science and Engineering

SP - 145

EP - 152

BT - Domain Decomposition Methods in Science and Engineering XXIII

A2 - Kim, Hyea Hyun

A2 - Klawonn, Axel

A2 - Park, Eun-Jae

A2 - Lee, Chang-Ock

A2 - Widlund, Olof B.

A2 - Cai, Xiao-Chuan

A2 - Keyes, David E.

PB - Springer Verlag

T2 - 23rd International Conference on Domain Decomposition Methods, DD23

Y2 - 6 July 2015 through 10 July 2015

ER -

Dolean V, Gander MJ, Veneros E, Zhang H. Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell’s equations. In Kim HH, Klawonn A, Park EJ, Lee CO, Widlund OB, Cai XC, Keyes DE, editors, Domain Decomposition Methods in Science and Engineering XXIII. Springer Verlag. 2017. p. 145-152. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-52389-7_13

Optimized Schwarz methods for heterogeneous Helmholtz and Maxwell’s equations

Abstract

Publication series

Conference

Access to Document

Other files and links

Cite this