Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data

Alexander Heinlein; Axel Klawonn; Martin Lanser; Janine Weber

doi:10.1007/978-3-030-56750-7_24

Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data

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

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

The convergence rate of classical domain decomposition methods for diffusion or elasticity problems usually deteriorates when large coefficient jumps occur along or across the interface between subdomains. In fact, the constant in the classical condition number bounds [11, 12] will depend on the coefficient jump.

Original language	English
Title of host publication	Domain Decomposition Methods in Science and Engineering XXV, DD 2018
Editors	Ronald Haynes, Scott MacLachlan, Xiao-Chuan Cai, Laurence Halpern, Hyea Hyun Kim, Axel Klawonn, Olof Widlund
Publisher	Springer
Pages	218-226
Number of pages	9
ISBN (Print)	9783030567491
DOIs	https://doi.org/10.1007/978-3-030-56750-7_24
Publication status	Published - 2020
Externally published	Yes
Event	25th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2018 - St. John's, Canada Duration: 23 Jul 2018 → 27 Jul 2018

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	138
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	25th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2018
Country/Territory	Canada
City	St. John's
Period	23/07/18 → 27/07/18

Access to Document

10.1007/978-3-030-56750-7_24

Cite this

Heinlein, A., Klawonn, A., Lanser, M., & Weber, J. (2020). Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data. In R. Haynes, S. MacLachlan, X.-C. Cai, L. Halpern, H. H. Kim, A. Klawonn, & O. Widlund (Eds.), Domain Decomposition Methods in Science and Engineering XXV, DD 2018 (pp. 218-226). (Lecture Notes in Computational Science and Engineering; Vol. 138). Springer. https://doi.org/10.1007/978-3-030-56750-7_24

Heinlein, Alexander ; Klawonn, Axel ; Lanser, Martin et al. / Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data. Domain Decomposition Methods in Science and Engineering XXV, DD 2018. editor / Ronald Haynes ; Scott MacLachlan ; Xiao-Chuan Cai ; Laurence Halpern ; Hyea Hyun Kim ; Axel Klawonn ; Olof Widlund. Springer, 2020. pp. 218-226 (Lecture Notes in Computational Science and Engineering).

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title = "Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data",

abstract = "The convergence rate of classical domain decomposition methods for diffusion or elasticity problems usually deteriorates when large coefficient jumps occur along or across the interface between subdomains. In fact, the constant in the classical condition number bounds [11, 12] will depend on the coefficient jump.",

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

year = "2020",

doi = "10.1007/978-3-030-56750-7_24",

language = "English",

isbn = "9783030567491",

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

publisher = "Springer",

pages = "218--226",

editor = "Ronald Haynes and Scott MacLachlan and Xiao-Chuan Cai and Laurence Halpern and Kim, {Hyea Hyun} and Axel Klawonn and Olof Widlund",

booktitle = "Domain Decomposition Methods in Science and Engineering XXV, DD 2018",

note = "25th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2018 ; Conference date: 23-07-2018 Through 27-07-2018",

}

Heinlein, A, Klawonn, A, Lanser, M & Weber, J 2020, Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data. in R Haynes, S MacLachlan, X-C Cai, L Halpern, HH Kim, A Klawonn & O Widlund (eds), Domain Decomposition Methods in Science and Engineering XXV, DD 2018. Lecture Notes in Computational Science and Engineering, vol. 138, Springer, pp. 218-226, 25th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2018, St. John's, Canada, 23/07/18. https://doi.org/10.1007/978-3-030-56750-7_24

Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data. / Heinlein, Alexander; Klawonn, Axel; Lanser, Martin et al.
Domain Decomposition Methods in Science and Engineering XXV, DD 2018. ed. / Ronald Haynes; Scott MacLachlan; Xiao-Chuan Cai; Laurence Halpern; Hyea Hyun Kim; Axel Klawonn; Olof Widlund. Springer, 2020. p. 218-226 (Lecture Notes in Computational Science and Engineering; Vol. 138).

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

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AU - Heinlein, Alexander

AU - Klawonn, Axel

AU - Lanser, Martin

AU - Weber, Janine

PY - 2020

Y1 - 2020

N2 - The convergence rate of classical domain decomposition methods for diffusion or elasticity problems usually deteriorates when large coefficient jumps occur along or across the interface between subdomains. In fact, the constant in the classical condition number bounds [11, 12] will depend on the coefficient jump.

AB - The convergence rate of classical domain decomposition methods for diffusion or elasticity problems usually deteriorates when large coefficient jumps occur along or across the interface between subdomains. In fact, the constant in the classical condition number bounds [11, 12] will depend on the coefficient jump.

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DO - 10.1007/978-3-030-56750-7_24

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AN - SCOPUS:85096543995

SN - 9783030567491

T3 - Lecture Notes in Computational Science and Engineering

SP - 218

EP - 226

BT - Domain Decomposition Methods in Science and Engineering XXV, DD 2018

A2 - Haynes, Ronald

A2 - MacLachlan, Scott

A2 - Cai, Xiao-Chuan

A2 - Halpern, Laurence

A2 - Kim, Hyea Hyun

A2 - Klawonn, Axel

A2 - Widlund, Olof

PB - Springer

T2 - 25th International Conference on Domain Decomposition Methods in Science and Engineering, DD 2018

Y2 - 23 July 2018 through 27 July 2018

ER -

Heinlein A, Klawonn A, Lanser M, Weber J. Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data. In Haynes R, MacLachlan S, Cai XC, Halpern L, Kim HH, Klawonn A, Widlund O, editors, Domain Decomposition Methods in Science and Engineering XXV, DD 2018. Springer. 2020. p. 218-226. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-56750-7_24

Machine Learning in Adaptive FETI-DP – A Comparison of Smart and Random Training Data

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