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Towards Textbook Efficiency for Parallel Multigrid

Published online by Cambridge University Press:  03 March 2015

Björn Gmeiner ,
Ulrich Rüde ,
Holger Stengel ,
Christian Waluga  and
Barbara Wohlmuth
Björn Gmeiner*
Affiliation:
Institute for Numerical Mathematics (M2), Technische Universität München, Boltzmannstrasse 3, D-85748 Garching b. München, Germany
Ulrich Rüde
Affiliation:
Department of Computer Science 10, FAU Erlangen-Nürnberg, Cauerstraße 6, D-91058 Erlangen, Germany
Holger Stengel
Affiliation:
Erlangen Regional Computing Center (RRZE), FAU Erlangen-Nürnberg, Martensstraße 1, D–91058 Erlangen, Germany
Christian Waluga
Affiliation:
Institute for Numerical Mathematics (M2), Technische Universität München, Boltzmannstrasse 3, D-85748 Garching b. München, Germany
Barbara Wohlmuth
Affiliation:
Institute for Numerical Mathematics (M2), Technische Universität München, Boltzmannstrasse 3, D-85748 Garching b. München, Germany
*
*Email addresses: [email protected] (B. Gmeiner), [email protected] (U. Rüde), [email protected] (C. Waluga), [email protected] (B. Wohlmuth)
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Abstract

In this work, we extend Achi Brandt's notion of textbook multigrid efficiency (TME) to massively parallel algorithms. Using a finite element based geometric multigrid implementation, we recall the classical view on TME with experiments for scalar linear equations with constant and varying coefficients as well as linear systems with saddle-point structure. To extend the idea of TME to the parallel setting, we give a new characterization of a work unit (WU) in an architecture-aware fashion by taking into account performance modeling techniques. We illustrate our newly introduced parallel TME measure by large-scale computations, solving problems with up to 200 billion unknowns on a TOP-10 supercomputer.

Keywords

65N5568W10Multigridparallel computingtextbook efficiencyfinite element method
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 1 , February 2015 , pp. 22 - 46
Copyright
Copyright © Global-Science Press 2015 

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