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2016 | OriginalPaper | Chapter

Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks

Authors : Allison H. Baker, Axel Klawonn, Tzanio Kolev, Martin Lanser, Oliver Rheinbach, Ulrike Meier Yang

Published in: Software for Exascale Computing - SPPEXA 2013-2015

Publisher: Springer International Publishing

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Abstract

The parallel performance of several classical Algebraic Multigrid (AMG) methods applied to linear elasticity problems is investigated. These methods include standard AMG approaches for systems of partial differential equations such as the unknown and hybrid approaches, as well as the more recent global matrix (GM) and local neighborhood (LN) approaches, which incorporate rigid body modes (RBMs) into the AMG interpolation operator. Numerical experiments are presented for both two- and three-dimensional elasticity problems on up to 131,072 cores (and 262,144 MPI processes) on the Vulcan supercomputer (LLNL, USA) and up to 262,144 cores (and 524,288 MPI processes) on the JUQUEEN supercomputer (JSC, Jülich, Germany). It is demonstrated that incorporating all RBMs into the interpolation leads generally to faster convergence and improved scalability.

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previous chapter One-Way and Fully-Coupled FE2 Methods for Heterogeneous Elasticity and Plasticity Problems: Parallel Scalability and an Application to Thermo-Elastoplasticity of Dual-Phase Steels
next chapter Recent Developments in the Theory and Application of the Sparse Grid Combination Technique
Literature
1.
Augustin, C.M., Neic, A., Liebmann, M., Prassl, A.J., Niederer, S.A., Haase, G., Plank, G.: Anatomically accurate high resolution modeling of human whole heart electromechanics: a strongly scalable algebraic multigrid solver method for nonlinear deformation. J. Comput. Phys. 305, 622–646 (2016)MathSciNetCrossRef
2.
3.
Blatt, M., Ippisch, O., Bastian, P.: A massively parallel algebraic multigrid preconditioner based on aggregation for elliptic problems with heterogeneous coefficients. arXiv preprint arXiv:1209.0960 (2013)
4.
5.
Braess, D.: Finite Elemente, vol. 4. Springer, Berlin (2007)MATH
6.
Brezina, M., Cleary, A.J., Falgout, R.D., Jones, J.E., Manteufel, T.A., McCormick, S.F., Ruge, J.W.: Algebraic multigrid based on element interpolation (AMGe). SIAM J. Sci. Comput. 22, 1570–1592 (2000). Also LLNL technical report UCRL-JC-131752
7.
Brezina, M., Tong, C., Becker, R.: Parallel algebraic multigrid methods for structural mechanics. SIAM J. Sci. Comput. 27 (5), 1534–1554 (2006)MathSciNetCrossRefMATH
8.
9.
Cleary, A.J., Falgout, R.D., Henson, V.E., Jones, J.E., Manteuffel, T.A., McCormick, S.F., Miranda, G.N., Ruge, J.W.: Robustness and scalability of algebraic multigrid. SIAM J. Sci. Comput. 21, 1886–1908 (2000)MathSciNetCrossRefMATH
10.
Clees, T.: AMG Strategies for ODE Systems with Applications in Industrial Semiconductor Simulation. Shaker Verlag GmbH, Germany (2005)
11.
12.
De Sterck, H., Falgout, R.D., Nolting, J.W., Yang, U.M.: Distance-two interpolation for parallel algebraic multigrid. Numer. Linear Algebra Appl. 15, 115–139 (2008)MathSciNetCrossRefMATH
13.
14.
Griebel, M., Oeltz, D., Schweitzer, A.: An algebraic multigrid for linear elasticity. J. Sci. Comput. 25 (2), 385–407 (2003)MathSciNetMATH
15.
16.
Henson, V.E., Yang, U.M.: BoomerAMG: a parallel algebraic multigrid solver and preconditioner. Appl. Numer. Math. 41, 155–177 (2002)MathSciNetCrossRefMATH
17.
18.
Lanser, M.: Nonlinear FETI-DP and BDDC Methods. Ph.D. thesis, Universität zu Köln (2015)
19.
20.
Notay, Y.: An aggregation-based algebraic multigrid method. Electron. Trans. Numer. Anal. 37, 123–146 (2010)MathSciNetMATH
21.
22.
Ruge, J.W.: AMG for problems of elasticity. Appl. Math. Comput. 19, 293–309 (1986)MATH
23.
Ruge, J.W., Stüben, K.: Algebraic multigrid (AMG). In: McCormick, S.F. (ed.) Multigrid Methods. Frontiers in Applied Mathematics, vol. 3, pp. 73–130. SIAM, Philadelphia (1987)CrossRef
24.
25.
Stüben, K.: An introduction to algebraic multigrid. In: Multigrid, pp. 413–532. Academic Press, London/San Diego (2001). also available as GMD Report 70, November 1999
26.
Trottenberg, U., Oosterlee, C.W., Schüller, A.: Multigrid. Academic Press, London/San Diego (2001)MATH
27.
Vaněk, P., Mandel, J., Brezina, M.: Algebraic multigrid by smooth aggregation for second and fourth order elliptic problems. Computing 56, 179–196 (1996)MathSciNetCrossRefMATH
28.
Yang, U.M.: Parallel algebraic multigrid methods – high performance preconditioners. In: Bruaset, A., Tveito, A. (eds.) Numerical Solutions of Partial Differential Equations on Parallel Computers. Lecture Notes in Computational Science and Engineering, pp. 209–236. Springer, Berlin (2006)CrossRef
29.
Yang, U.M.: On long-range interpolation operators for aggressive coarsening. Numer. Linear Algebra Appl. 17, 453–472 (2010)MathSciNetMATH
Metadata
Title
Scalability of Classical Algebraic Multigrid for Elasticity to Half a Million Parallel Tasks
Authors
Allison H. Baker
Axel Klawonn
Tzanio Kolev
Martin Lanser
Oliver Rheinbach
Ulrike Meier Yang
Copyright Year
2016
Book
Software for Exascale Computing - SPPEXA 2013-2015

Print ISBN: 978-3-319-40526-1

Electronic ISBN: 978-3-319-40528-5

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-40528-5_6

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