Towards Textbook Efficiency for Parallel Multigrid

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 coeff...

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Bibliographic Details
Published inNumerical Mathematics: Theory, Methods and Applications Vol. 8; no. 1; pp. 22 - 46
Main Authors Gmeiner, Björn, Rüde, Ulrich, Stengel, Holger, Waluga, Christian, Wohlmuth, Barbara
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2015
Subjects
finite element method
Multigrid
65N55
parallel computing
textbook efficiency
68W10
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Summary: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.
ISSN:1004-8979
2079-7338
DOI:10.4208/nmtma.2015.w10si