A quantitative performance analysis for Stokes solvers at the extreme scale.

Gmeiner B, Huber M, John L, Rüde U, Wohlmuth BI (2015)

Publication Language: English

Publication Type: Other publication type

Publication year: 2015

City/Town: arXiv

Open Access Link: http://arxiv.org/pdf/1511.02134v1.pdf

Abstract

This article presents a systematic quantitative performance analysis for large finite element computations on extreme scale computing systems. Three parallel iterative solvers for the Stokes system, discretized by low order tetrahedral elements, are compared with respect to their numerical efficiency and their scalability running on up to 786 432 parallel threads. A genuine multigrid method for the saddle point system using an Uzawa-type smoother provides the best overall performance with respect to memory consumption and time-to-solution. The largest system solved on a Blue Gene/Q system has more than ten trillion (1.1 · 1013) unknowns and requires about 13 minutes compute time. Despite the matrix free and highly optimized implementation, the memory requirement for the solution vector and the auxiliary vectors is about 200 TByte. Brandt’s notion of “textbook multigrid efficiency” is employed to study the algorithmic performance of iterative solvers. A recent extension of this paradigm to “parallel textbook multigrid efficiency” makes it possible to assess also the efficiency of parallel iterative solvers for a given hardware architecture in absolute terms. The efficiency of the method is demonstrated for simulating incompressible fluid flow in a pipe filled with spherical obstacles.

Authors with CRIS profile

Björn Gmeiner Lehrstuhl für Informatik 10 (Systemsimulation) (LSS) Markus Huber Lehrstuhl für Informatik 10 (Systemsimulation) (LSS) Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)

Involved external institutions

Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Gmeiner, B., Huber, M., John, L., Rüde, U., & Wohlmuth, B.I. (2015). A quantitative performance analysis for Stokes solvers at the extreme scale. arXiv.

MLA:

Gmeiner, Björn, et al. A quantitative performance analysis for Stokes solvers at the extreme scale. arXiv, 2015.

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