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Title
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Improving the arithmetic intensity of multigrid with the help of polynomial smoothers
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Author
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Abstract
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| The basic building blocks of a classic multigrid algorithm, which are essentially stencil computations, all have a low ratio of executed floating point operations per byte fetched from memory. This important ratio can be identified as the arithmetic intensity. Applications with a low arithmetic intensity are typically bounded by memory traffic and achieve only a small percentage of the theoretical peak performance of the underlying hardware. We propose a polynomial Chebyshev smoother, which we implement using cache-aware tiling, to increase the arithmetic intensity of a multigrid V-cycle. This tiling approach involves a trade-off between redundant computations and cache misses. Unlike common conception, we observe optimal performance for higher degrees of the smoother. The higher-degree polynomial Chebyshev smoother can be used to smooth more than just the upper half of the error frequencies, leading to better V-cycle convergence rates. Smoothing more than the upper half of the error spectrum allows a more aggressive coarsening approach where some levels in the multigrid hierarchy are skipped. Copyright (C) 2012 John Wiley & Sons, Ltd. |
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Language
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English
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Source (journal)
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Numerical linear algebra with applications. - Chichester
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Publication
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Chichester
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Wiley
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2012
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ISSN
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1070-5325
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DOI
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10.1002/NLA.1808
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Volume/pages
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19
:2
(2012)
, p. 253-267
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ISI
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000299777500006
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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