Title
Improving the arithmetic intensity of multigrid with the help of polynomial smoothers Improving the arithmetic intensity of multigrid with the help of polynomial smoothers
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Chichester :Wiley ,
Subject
Mathematics
Source (journal)
Numerical linear algebra with applications. - Chichester
Volume/pages
19(2012) :2 , p. 253-267
ISSN
1070-5325
ISI
000299777500006
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
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.
E-info
https://repository.uantwerpen.be/docman/iruaauth/130460/e111219.pdf
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000299777500006&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000299777500006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000299777500006&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848
Handle