Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach

Claudio Tomasi; Rolf Krause

doi:10.1007/978-3-030-95025-5_63

Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach

Claudio Tomasi^*, Rolf Krause

^*Corresponding author for this work

Applied Mathematics and Computational Science

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

Abstract

Multigrid (MG) methods are among the most successful strategies for solving linearsystems arising from discretized elliptic equations. The main idea is to combinedifferent levels of approximation in a multilevel hierarchy to compute the solution:it is possible to show that this algorithm is effective on the entire spectrum, thusleading to an optimal convergence property [2, 3].

Original language	English (US)
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 Science and Business Media Deutschland GmbH
Pages	579-587
Number of pages	9
ISBN (Print)	9783030950248
DOIs	https://doi.org/10.1007/978-3-030-95025-5_63
State	Published - 2022
Event	26th International Conference on Domain Decomposition Methods, 2020 - Virtual, Online Duration: Dec 7 2020 → Dec 12 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	12/7/20 → 12/12/20

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

ASJC Scopus subject areas

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

Access to Document

10.1007/978-3-030-95025-5_63

Cite this

Tomasi, C., & Krause, R. (2022). Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach. In S. C. Brenner, A. Klawonn, J. Xu, E. Chung, J. Zou, & F. Kwok (Eds.), Domain Decomposition Methods in Science and Engineering XXVI (pp. 579-587). (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_63

Tomasi, Claudio ; Krause, Rolf. / Construction of Grid Operators for Multilevel Solvers : a Neural Network Approach. Domain Decomposition Methods in Science and Engineering XXVI. editor / Susanne C. Brenner ; Axel Klawonn ; Jinchao Xu ; Eric Chung ; Jun Zou ; Felix Kwok. Springer Science and Business Media Deutschland GmbH, 2022. pp. 579-587 (Lecture Notes in Computational Science and Engineering).

@inproceedings{cd0153877ede4123a1c9605ad674b01f,

title = "Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach",

abstract = "Multigrid (MG) methods are among the most successful strategies for solving linearsystems arising from discretized elliptic equations. The main idea is to combinedifferent levels of approximation in a multilevel hierarchy to compute the solution:it is possible to show that this algorithm is effective on the entire spectrum, thusleading to an optimal convergence property [2, 3].",

author = "Claudio Tomasi and Rolf Krause",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 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_63",

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Tomasi, C & Krause, R 2022, Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach. 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, pp. 579-587, 26th International Conference on Domain Decomposition Methods, 2020, Virtual, Online, 12/7/20. https://doi.org/10.1007/978-3-030-95025-5_63

Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach. / Tomasi, Claudio; Krause, Rolf.
Domain Decomposition Methods in Science and Engineering XXVI. ed. / Susanne C. Brenner; Axel Klawonn; Jinchao Xu; Eric Chung; Jun Zou; Felix Kwok. Springer Science and Business Media Deutschland GmbH, 2022. p. 579-587 (Lecture Notes in Computational Science and Engineering; Vol. 145).

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

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AU - Krause, Rolf

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BT - Domain Decomposition Methods in Science and Engineering XXVI

A2 - Brenner, Susanne C.

A2 - Klawonn, Axel

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A2 - Zou, Jun

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Tomasi C, Krause R. Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach. In Brenner SC, Klawonn A, Xu J, Chung E, Zou J, Kwok F, editors, Domain Decomposition Methods in Science and Engineering XXVI. Springer Science and Business Media Deutschland GmbH. 2022. p. 579-587. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-95025-5_63

Construction of Grid Operators for Multilevel Solvers: a Neural Network Approach

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ASJC Scopus subject areas

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