Publication
Title
Improving the arithmetic intensity of multigrid with the help of polynomial smoothers
Author
Abstract
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.
Language
English
Source (journal)
Numerical linear algebra with applications. - Chichester
Publication
Chichester : Wiley, 2012
ISSN
1070-5325
Volume/pages
19:2(2012), p. 253-267
ISI
000299777500006
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 05.03.2012
Last edited 24.06.2017
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