Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning

Alexander Heinlein; Axel Klawonn; Martin Lanser; Janine Weber

doi:10.1007/978-3-030-95025-5_32

Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning

Alexander Heinlein^*, Axel Klawonn, Martin Lanser, Janine Weber

^*Corresponding author for this work

Numerical Analysis

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

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Abstract

For complex model problems with coefficient or material distributions with large jumps along or across the domain decomposition interface, the convergence rate of classic domain decomposition methods for scalar elliptic problems usually deteriorates. In particular, the classic condition number bounds [1, 12] will depend on the contrast of the coefficient function. As a remedy, different adaptive coarse spaces, e.g. [4, 13], have been developed which are obtained by solving certain generalized eigenvalue problems on local parts of the interface, i.e., edges and/or faces.

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	307-315
Number of pages	9
ISBN (Print)	9783030950248
DOIs	https://doi.org/10.1007/978-3-030-95025-5_32
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

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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978-3-030-95025-5_32Final published version, 1.43 MB

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Heinlein, A., Klawonn, A., Lanser, M., & Weber, J. (2022). Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning. In S. C. Brenner, A. Klawonn, J. Xu, E. Chung, J. Zou, & F. Kwok (Eds.), Domain Decomposition Methods in Science and Engineering XXVI (pp. 307-315). (Lecture Notes in Computational Science and Engineering; Vol. 145). Springer. https://doi.org/10.1007/978-3-030-95025-5_32

Heinlein, Alexander ; Klawonn, Axel ; Lanser, Martin et al. / Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning. Domain Decomposition Methods in Science and Engineering XXVI. editor / Susanne C. Brenner ; Axel Klawonn ; Jinchao Xu ; Eric Chung ; Jun Zou ; Felix Kwok. Springer, 2022. pp. 307-315 (Lecture Notes in Computational Science and Engineering).

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title = "Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning",

abstract = "For complex model problems with coefficient or material distributions with large jumps along or across the domain decomposition interface, the convergence rate of classic domain decomposition methods for scalar elliptic problems usually deteriorates. In particular, the classic condition number bounds [1, 12] will depend on the contrast of the coefficient function. As a remedy, different adaptive coarse spaces, e.g. [4, 13], have been developed which are obtained by solving certain generalized eigenvalue problems on local parts of the interface, i.e., edges and/or faces.",

author = "Alexander Heinlein and Axel Klawonn and Martin Lanser and Janine Weber",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. ; 26th International Conference on Domain Decomposition Methods, 2020 ; Conference date: 07-12-2020 Through 12-12-2020",

year = "2022",

doi = "10.1007/978-3-030-95025-5_32",

language = "English",

isbn = "9783030950248",

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

publisher = "Springer",

pages = "307--315",

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",

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Heinlein, A, Klawonn, A, Lanser, M & Weber, J 2022, Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning. 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. 307-315, 26th International Conference on Domain Decomposition Methods, 2020, Virtual, Online, 7/12/20. https://doi.org/10.1007/978-3-030-95025-5_32

Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning. / Heinlein, Alexander; Klawonn, Axel; Lanser, Martin 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. 307-315 (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 - Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning

AU - Heinlein, Alexander

AU - Klawonn, Axel

AU - Lanser, Martin

AU - Weber, Janine

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2022

Y1 - 2022

N2 - For complex model problems with coefficient or material distributions with large jumps along or across the domain decomposition interface, the convergence rate of classic domain decomposition methods for scalar elliptic problems usually deteriorates. In particular, the classic condition number bounds [1, 12] will depend on the contrast of the coefficient function. As a remedy, different adaptive coarse spaces, e.g. [4, 13], have been developed which are obtained by solving certain generalized eigenvalue problems on local parts of the interface, i.e., edges and/or faces.

AB - For complex model problems with coefficient or material distributions with large jumps along or across the domain decomposition interface, the convergence rate of classic domain decomposition methods for scalar elliptic problems usually deteriorates. In particular, the classic condition number bounds [1, 12] will depend on the contrast of the coefficient function. As a remedy, different adaptive coarse spaces, e.g. [4, 13], have been developed which are obtained by solving certain generalized eigenvalue problems on local parts of the interface, i.e., edges and/or faces.

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BT - Domain Decomposition Methods in Science and Engineering XXVI

A2 - Brenner, Susanne C.

A2 - Klawonn, Axel

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Heinlein A, Klawonn A, Lanser M, Weber J. Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning. In Brenner SC, Klawonn A, Xu J, Chung E, Zou J, Kwok F, editors, Domain Decomposition Methods in Science and Engineering XXVI. Springer. 2022. p. 307-315. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-95025-5_32

Predicting the Geometric Location of Critical Edges in Adaptive GDSW Overlapping Domain Decomposition Methods Using Deep Learning

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