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 cacheaware tiling, to increase the arithmetic intensity of a multigrid Vcycle. This tiling approach involves a tradeoff between redundant computations and cache misses. Unlike common conception, we observe optimal performance for higher degrees of the smoother. The higherdegree polynomial Chebyshev smoother can be used to smooth more than just the upper half of the error frequencies, leading to better Vcycle 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 



10705325
 
Volume/pages 



19:2(2012), p. 253267
 
ISI 



000299777500006
 
Full text (Publishers DOI) 


  
Full text (publishers version  intranet only) 


  
