A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance

Simon Bauer; Markus Huber; Marcus Mohr; Ulrich Rüde; Barbara Wohlmuth

doi:10.1007/978-3-319-93701-4_2

A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance

Simon Bauer, Markus Huber, Marcus Mohr, Ulrich Rüde, Barbara Wohlmuth

Chair of Numerical Analysis

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

9 Scopus citations

Abstract

We report on a two-scale approach for efficient matrix-free finite element simulations. The proposed method is based on surrogate element matrices constructed by low-order polynomial approximations. It is applied to a Stokes-type PDE system with variable viscosity as is a key component in mantle convection models. We set the ground for a rigorous performance analysis inspired by the concept of parallel textbook multigrid efficiency and study the weak scaling behavior on SuperMUC, a peta-scale supercomputer system. For a complex geodynamical model, we achieve a parallel efficiency of 95% on up to 47 250 compute cores. Our largest simulation uses a trillion (O10¹²)) degrees of freedom for a global mesh resolution of 1.7 km.

Original language	English
Title of host publication	Computational Science – ICCS 2018 - 18th International Conference, Proceedings
Editors	Valeria V. Krzhizhanovskaya, Michael Harold Lees, Peter M. Sloot, Jack Dongarra, Yong Shi, Yingjie Tian, Haohuan Fu
Publisher	Springer Verlag
Pages	17-30
Number of pages	14
ISBN (Print)	9783319937007
DOIs	https://doi.org/10.1007/978-3-319-93701-4_2
State	Published - 2018
Event	18th International Conference on Computational Science, ICCS 2018 - Wuxi, China Duration: 11 Jun 2018 → 13 Jun 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10861 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th International Conference on Computational Science, ICCS 2018
Country/Territory	China
City	Wuxi
Period	11/06/18 → 13/06/18

Keywords

Large scale geophysical application
Massively parallel multigrid
Matrix-free on-the-fly assembly
Two-scale PDE discretization

Access to Document

10.1007/978-3-319-93701-4_2

Cite this

Bauer, S., Huber, M., Mohr, M., Rüde, U., & Wohlmuth, B. (2018). A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance. In V. V. Krzhizhanovskaya, M. H. Lees, P. M. Sloot, J. Dongarra, Y. Shi, Y. Tian, & H. Fu (Eds.), Computational Science – ICCS 2018 - 18th International Conference, Proceedings (pp. 17-30). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10861 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-93701-4_2

Bauer, Simon ; Huber, Markus ; Mohr, Marcus et al. / A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance. Computational Science – ICCS 2018 - 18th International Conference, Proceedings. editor / Valeria V. Krzhizhanovskaya ; Michael Harold Lees ; Peter M. Sloot ; Jack Dongarra ; Yong Shi ; Yingjie Tian ; Haohuan Fu. Springer Verlag, 2018. pp. 17-30 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance",

abstract = "We report on a two-scale approach for efficient matrix-free finite element simulations. The proposed method is based on surrogate element matrices constructed by low-order polynomial approximations. It is applied to a Stokes-type PDE system with variable viscosity as is a key component in mantle convection models. We set the ground for a rigorous performance analysis inspired by the concept of parallel textbook multigrid efficiency and study the weak scaling behavior on SuperMUC, a peta-scale supercomputer system. For a complex geodynamical model, we achieve a parallel efficiency of 95% on up to 47 250 compute cores. Our largest simulation uses a trillion (O1012)) degrees of freedom for a global mesh resolution of 1.7 km.",

keywords = "Large scale geophysical application, Massively parallel multigrid, Matrix-free on-the-fly assembly, Two-scale PDE discretization",

author = "Simon Bauer and Markus Huber and Marcus Mohr and Ulrich R{\"u}de and Barbara Wohlmuth",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 18th International Conference on Computational Science, ICCS 2018 ; Conference date: 11-06-2018 Through 13-06-2018",

year = "2018",

doi = "10.1007/978-3-319-93701-4_2",

language = "English",

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Bauer, S, Huber, M, Mohr, M, Rüde, U & Wohlmuth, B 2018, A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance. in VV Krzhizhanovskaya, MH Lees, PM Sloot, J Dongarra, Y Shi, Y Tian & H Fu (eds), Computational Science – ICCS 2018 - 18th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10861 LNCS, Springer Verlag, pp. 17-30, 18th International Conference on Computational Science, ICCS 2018, Wuxi, China, 11/06/18. https://doi.org/10.1007/978-3-319-93701-4_2

A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance. / Bauer, Simon; Huber, Markus; Mohr, Marcus et al.
Computational Science – ICCS 2018 - 18th International Conference, Proceedings. ed. / Valeria V. Krzhizhanovskaya; Michael Harold Lees; Peter M. Sloot; Jack Dongarra; Yong Shi; Yingjie Tian; Haohuan Fu. Springer Verlag, 2018. p. 17-30 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10861 LNCS).

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

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T1 - A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance

AU - Bauer, Simon

AU - Huber, Markus

AU - Mohr, Marcus

AU - Rüde, Ulrich

AU - Wohlmuth, Barbara

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - We report on a two-scale approach for efficient matrix-free finite element simulations. The proposed method is based on surrogate element matrices constructed by low-order polynomial approximations. It is applied to a Stokes-type PDE system with variable viscosity as is a key component in mantle convection models. We set the ground for a rigorous performance analysis inspired by the concept of parallel textbook multigrid efficiency and study the weak scaling behavior on SuperMUC, a peta-scale supercomputer system. For a complex geodynamical model, we achieve a parallel efficiency of 95% on up to 47 250 compute cores. Our largest simulation uses a trillion (O1012)) degrees of freedom for a global mesh resolution of 1.7 km.

AB - We report on a two-scale approach for efficient matrix-free finite element simulations. The proposed method is based on surrogate element matrices constructed by low-order polynomial approximations. It is applied to a Stokes-type PDE system with variable viscosity as is a key component in mantle convection models. We set the ground for a rigorous performance analysis inspired by the concept of parallel textbook multigrid efficiency and study the weak scaling behavior on SuperMUC, a peta-scale supercomputer system. For a complex geodynamical model, we achieve a parallel efficiency of 95% on up to 47 250 compute cores. Our largest simulation uses a trillion (O1012)) degrees of freedom for a global mesh resolution of 1.7 km.

KW - Large scale geophysical application

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AN - SCOPUS:85049069840

SN - 9783319937007

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Computational Science – ICCS 2018 - 18th International Conference, Proceedings

A2 - Krzhizhanovskaya, Valeria V.

A2 - Lees, Michael Harold

A2 - Sloot, Peter M.

A2 - Dongarra, Jack

A2 - Shi, Yong

A2 - Tian, Yingjie

A2 - Fu, Haohuan

PB - Springer Verlag

T2 - 18th International Conference on Computational Science, ICCS 2018

Y2 - 11 June 2018 through 13 June 2018

ER -

Bauer S, Huber M, Mohr M, Rüde U, Wohlmuth B. A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance. In Krzhizhanovskaya VV, Lees MH, Sloot PM, Dongarra J, Shi Y, Tian Y, Fu H, editors, Computational Science – ICCS 2018 - 18th International Conference, Proceedings. Springer Verlag. 2018. p. 17-30. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-93701-4_2

A New Matrix-Free Approach for Large-Scale Geodynamic Simulations and its Performance

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