Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems

N. Bootland; V. Dwarka; P. Jolivet; V. Dolean; C. Vuik

doi:10.1007/978-3-030-95025-5_11

Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems

N. Bootland^*, V. Dwarka, P. Jolivet, V. Dolean, C. Vuik

^*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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Abstract

In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, the resulting linear system after discretisation becomes indefinite and tailored iterative solvers are required to obtain the numerical solution efficiently. At the same time, the mesh must be kept fine enough in order to prevent numerical dispersion ‘polluting’ the solution [4]. This leads to very large linear systems, further amplifying the need to develop economical solver methodologies.

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
Publisher	Springer
Pages	127-135
Number of pages	9
ISBN (Print)	9783030950248
DOIs	https://doi.org/10.1007/978-3-030-95025-5_11
Publication status	Published - 2022
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

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10.1007/978-3-030-95025-5_11

978-3-030-95025-5_11Final published version, 1.18 MBLicence: CC BY

Cite this

Bootland, N., Dwarka, V., Jolivet, P., Dolean, V., & Vuik, C. (2022). Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems. In S. C. Brenner, A. Klawonn, J. Xu, E. Chung, J. Zou, & F. Kwok (Eds.), Domain Decomposition Methods in Science and Engineering XXVI (pp. 127-135). (Lecture Notes in Computational Science and Engineering; Vol. 145). Springer. https://doi.org/10.1007/978-3-030-95025-5_11

@inproceedings{5670e4d3d5954b5bbe425047cd643cbf,

title = "Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems",

abstract = "In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, the resulting linear system after discretisation becomes indefinite and tailored iterative solvers are required to obtain the numerical solution efficiently. At the same time, the mesh must be kept fine enough in order to prevent numerical dispersion {\textquoteleft}polluting{\textquoteright} the solution [4]. This leads to very large linear systems, further amplifying the need to develop economical solver methodologies.",

author = "N. Bootland and V. Dwarka and P. Jolivet and V. Dolean and C. Vuik",

year = "2022",

doi = "10.1007/978-3-030-95025-5_11",

language = "English",

isbn = "9783030950248",

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

publisher = "Springer",

pages = "127--135",

editor = "Brenner, {Susanne C.} and Axel Klawonn and Jinchao Xu and Eric Chung and Jun Zou and Felix Kwok",

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

note = "26th International Conference on Domain Decomposition Methods, 2020 ; Conference date: 07-12-2020 Through 12-12-2020",

}

Bootland, N, Dwarka, V, Jolivet, P, Dolean, V & Vuik, C 2022, Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems. 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, pp. 127-135, 26th International Conference on Domain Decomposition Methods, 2020, Virtual, Online, 7/12/20. https://doi.org/10.1007/978-3-030-95025-5_11

Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems. / Bootland, N.; Dwarka, V.; Jolivet, P. et al.
Domain Decomposition Methods in Science and Engineering XXVI. ed. / Susanne C. Brenner; Axel Klawonn; Jinchao Xu; Eric Chung; Jun Zou; Felix Kwok. Springer, 2022. p. 127-135 (Lecture Notes in Computational Science and Engineering; Vol. 145).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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T1 - Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems

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AU - Dwarka, V.

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AU - Dolean, V.

AU - Vuik, C.

PY - 2022

Y1 - 2022

N2 - In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, the resulting linear system after discretisation becomes indefinite and tailored iterative solvers are required to obtain the numerical solution efficiently. At the same time, the mesh must be kept fine enough in order to prevent numerical dispersion ‘polluting’ the solution [4]. This leads to very large linear systems, further amplifying the need to develop economical solver methodologies.

AB - In recent years, domain decomposition based preconditioners have become popular tools to solve the Helmholtz equation. Notorious for causing a variety of convergence issues, the Helmholtz equation remains a challenging PDE to solve numerically. Even for simple model problems, the resulting linear system after discretisation becomes indefinite and tailored iterative solvers are required to obtain the numerical solution efficiently. At the same time, the mesh must be kept fine enough in order to prevent numerical dispersion ‘polluting’ the solution [4]. This leads to very large linear systems, further amplifying the need to develop economical solver methodologies.

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ER -

Inexact Subdomain Solves Using Deflated GMRES for Helmholtz Problems

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