A high-performance implementation of a robust preconditioner for heterogeneous problems

Linus Seelinger; Anne Reinarz; Robert Scheichl

doi:10.1007/978-3-030-43229-4_11

A high-performance implementation of a robust preconditioner for heterogeneous problems

Linus Seelinger, Anne Reinarz, Robert Scheichl

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

1 Citation (SciVal)

Abstract

We present an efficient implementation of the highly robust and scalable GenEO (Generalized Eigenproblems in the Overlap) preconditioner [16] in the high-performance PDE framework DUNE [6]. The GenEO coarse space is constructed by combining low energy solutions of a local generalised eigenproblem using a partition of unity. The main contribution of this paper is documenting the technical details that are crucial to the efficiency of a high-performance implementation of the GenEO preconditioner. We demonstrate both weak and strong scaling for the GenEO solver on over 15, 000 cores by solving an industrially motivated problem in aerospace engineering. Further, we show that for highly complex parameter distributions arising in certain real-world applications, established methods become intractable while GenEO remains fully effective.

Original language	English
Title of host publication	Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Revised Selected Papers
Editors	Roman Wyrzykowski, Konrad Karczewski, Ewa Deelman, Jack Dongarra
Publisher	Springer
Pages	117-128
Number of pages	12
ISBN (Print)	9783030432287
DOIs	https://doi.org/10.1007/978-3-030-43229-4_11
Publication status	Published - 2020
Event	13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019 - Bialystok, Poland Duration: 8 Sept 2019 → 11 Sept 2019

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12043 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019
Country/Territory	Poland
City	Bialystok
Period	8/09/19 → 11/09/19

Bibliographical note

Funding Information:
This work was supported by an EPSRC Maths for Manufacturing grant (EP/K031368/1). This research made use of the Balena High Performance Computing Service at the University of Bath. This work used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk).

Funding Information:
Acknowledgements. This work was supported by an EPSRC Maths for Manufacturing grant (EP/K031368/1). This research made use of the Balena High Performance Computing Service at the University of Bath. This work used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk).

Publisher Copyright:
© Springer Nature Switzerland AG 2020.

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

Domain decomposition
High performance computing
Partial differential equations
Preconditioning

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-030-43229-4_11

Cite this

Seelinger, L., Reinarz, A., & Scheichl, R. (2020). A high-performance implementation of a robust preconditioner for heterogeneous problems. In R. Wyrzykowski, K. Karczewski, E. Deelman, & J. Dongarra (Eds.), Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Revised Selected Papers (pp. 117-128). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12043 LNCS). Springer. https://doi.org/10.1007/978-3-030-43229-4_11

A high-performance implementation of a robust preconditioner for heterogeneous problems. / Seelinger, Linus; Reinarz, Anne; Scheichl, Robert.
Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Revised Selected Papers. ed. / Roman Wyrzykowski; Konrad Karczewski; Ewa Deelman; Jack Dongarra. Springer, 2020. p. 117-128 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12043 LNCS).

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

Seelinger, L, Reinarz, A & Scheichl, R 2020, A high-performance implementation of a robust preconditioner for heterogeneous problems. in R Wyrzykowski, K Karczewski, E Deelman & J Dongarra (eds), Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12043 LNCS, Springer, pp. 117-128, 13th International Conference on Parallel Processing and Applied Mathematics, PPAM 2019, Bialystok, Poland, 8/09/19. https://doi.org/10.1007/978-3-030-43229-4_11

Seelinger L, Reinarz A, Scheichl R. A high-performance implementation of a robust preconditioner for heterogeneous problems. In Wyrzykowski R, Karczewski K, Deelman E, Dongarra J, editors, Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Revised Selected Papers. Springer. 2020. p. 117-128. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2020 Mar 19. doi: 10.1007/978-3-030-43229-4_11

Seelinger, Linus ; Reinarz, Anne ; Scheichl, Robert. / A high-performance implementation of a robust preconditioner for heterogeneous problems. Parallel Processing and Applied Mathematics - 13th International Conference, PPAM 2019, Revised Selected Papers. editor / Roman Wyrzykowski ; Konrad Karczewski ; Ewa Deelman ; Jack Dongarra. Springer, 2020. pp. 117-128 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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A high-performance implementation of a robust preconditioner for heterogeneous problems

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Multiscale Modelling of Aerospace Composites

Cite this

A high-performance implementation of a robust preconditioner for heterogeneous problems

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Multiscale Modelling of Aerospace Composites

Cite this