A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem

Shihua Gong; Martin J. Gander; Ivan G. Graham; Euan A. Spence

doi:10.1007/978-3-030-95025-5_30

A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem

Shihua Gong, Martin J. Gander, Ivan G. Graham, Euan A. Spence

University of Geneva

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Abstract

Method (5)–(8) is an example of methods studied more generally in the Optimized Schwarz literature (e.g., [4, 10]), where Robin (or more sophisticated) transmission conditions are constructed with the aim of optimizing convergence rates. Although the transmission condition (6) above can be justified directly as a first order absorbing condition for the local Helmholtz problem (5) (without considering optimization), this method is still often called ‘OptimizedRestrictedAdditive Schwarz’ (or ‘ORAS’) and we shall continue this naming convention here. ORAS is arguably the most successful one-level parallel method for Helmholtz problems.

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XXVI
Editors	Susanne C. Brenner, Axel Klawonn, Jinchao Xu, Eric Chung, Jun Zou, Felix Kwok
Place of Publication	Germany
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	291-298
Number of pages	8
ISBN (Print)	9783030950248
DOIs	https://doi.org/10.1007/978-3-030-95025-5_30
Publication status	Published - 16 Mar 2023
Event	26th International Conference on Domain Decomposition Methods, 2020 - Virtual, Online Duration: 7 Dec 2020 → 12 Dec 2020

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	145
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	26th International Conference on Domain Decomposition Methods, 2020
City	Virtual, Online
Period	7/12/20 → 12/12/20

ASJC Scopus subject areas

Modelling and Simulation
General Engineering
Discrete Mathematics and Combinatorics
Control and Optimization
Computational Mathematics

Access to Document

10.1007/978-3-030-95025-5_30

Cite this

Gong, S., Gander, M. J., Graham, I. G., & Spence, E. A. (2023). A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem. In S. C. Brenner, A. Klawonn, J. Xu, E. Chung, J. Zou, & F. Kwok (Eds.), Domain Decomposition Methods in Science and Engineering XXVI (pp. 291-298). (Lecture Notes in Computational Science and Engineering; Vol. 145). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-95025-5_30

A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem. / Gong, Shihua; Gander, Martin J.; Graham, Ivan G. et al.
Domain Decomposition Methods in Science and Engineering XXVI. ed. / Susanne C. Brenner; Axel Klawonn; Jinchao Xu; Eric Chung; Jun Zou; Felix Kwok. Germany: Springer Science and Business Media Deutschland GmbH, 2023. p. 291-298 (Lecture Notes in Computational Science and Engineering; Vol. 145).

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

Gong, S, Gander, MJ, Graham, IG & Spence, EA 2023, A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem. in SC Brenner, A Klawonn, J Xu, E Chung, J Zou & F Kwok (eds), Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol. 145, Springer Science and Business Media Deutschland GmbH, Germany, pp. 291-298, 26th International Conference on Domain Decomposition Methods, 2020, Virtual, Online, 7/12/20. https://doi.org/10.1007/978-3-030-95025-5_30

Gong S, Gander MJ, Graham IG , Spence EA. A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem. In Brenner SC, Klawonn A, Xu J, Chung E, Zou J, Kwok F, editors, Domain Decomposition Methods in Science and Engineering XXVI. Germany: Springer Science and Business Media Deutschland GmbH. 2023. p. 291-298. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-95025-5_30

Gong, Shihua ; Gander, Martin J. ; Graham, Ivan G. et al. / A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem. Domain Decomposition Methods in Science and Engineering XXVI. editor / Susanne C. Brenner ; Axel Klawonn ; Jinchao Xu ; Eric Chung ; Jun Zou ; Felix Kwok. Germany : Springer Science and Business Media Deutschland GmbH, 2023. pp. 291-298 (Lecture Notes in Computational Science and Engineering).

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abstract = "Method (5)–(8) is an example of methods studied more generally in the Optimized Schwarz literature (e.g., [4, 10]), where Robin (or more sophisticated) transmission conditions are constructed with the aim of optimizing convergence rates. Although the transmission condition (6) above can be justified directly as a first order absorbing condition for the local Helmholtz problem (5) (without considering optimization), this method is still often called {\textquoteleft}OptimizedRestrictedAdditive Schwarz{\textquoteright} (or {\textquoteleft}ORAS{\textquoteright}) and we shall continue this naming convention here. ORAS is arguably the most successful one-level parallel method for Helmholtz problems.",

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AB - Method (5)–(8) is an example of methods studied more generally in the Optimized Schwarz literature (e.g., [4, 10]), where Robin (or more sophisticated) transmission conditions are constructed with the aim of optimizing convergence rates. Although the transmission condition (6) above can be justified directly as a first order absorbing condition for the local Helmholtz problem (5) (without considering optimization), this method is still often called ‘OptimizedRestrictedAdditive Schwarz’ (or ‘ORAS’) and we shall continue this naming convention here. ORAS is arguably the most successful one-level parallel method for Helmholtz problems.

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A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem

Abstract

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ASJC Scopus subject areas

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Fast solvers for frequency-domain wave-scattering problems and applications

At the interface between semiclassical analysis and numerical analysis of Wave propogation problems

Cite this

A Variational Interpretation of Restricted Additive Schwarz With Impedance Transmission Condition for the Helmholtz Problem

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Fast solvers for frequency-domain wave-scattering problems and applications

At the interface between semiclassical analysis and numerical analysis of Wave propogation problems

Cite this