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  1. Transactions on Mathematical Software (TOMS)
  2. ACM Transactions on Mathematical Software (TOMS) : Volume 26
  3. Issue 2(Special issue in honor of John Rice's 65th birthday), June 2000
  4. How to vectorize the algebraic multilevel iteration
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ACM Transactions on Mathematical Software (TOMS) : Volume 43
ACM Transactions on Mathematical Software (TOMS) : Volume 42
ACM Transactions on Mathematical Software (TOMS) : Volume 41
ACM Transactions on Mathematical Software (TOMS) : Volume 40
ACM Transactions on Mathematical Software (TOMS) : Volume 39
ACM Transactions on Mathematical Software (TOMS) : Volume 38
ACM Transactions on Mathematical Software (TOMS) : Volume 37
ACM Transactions on Mathematical Software (TOMS) : Volume 36
ACM Transactions on Mathematical Software (TOMS) : Volume 35
ACM Transactions on Mathematical Software (TOMS) : Volume 34
ACM Transactions on Mathematical Software (TOMS) : Volume 33
ACM Transactions on Mathematical Software (TOMS) : Volume 32
ACM Transactions on Mathematical Software (TOMS) : Volume 31
ACM Transactions on Mathematical Software (TOMS) : Volume 30
ACM Transactions on Mathematical Software (TOMS) : Volume 29
ACM Transactions on Mathematical Software (TOMS) : Volume 28
ACM Transactions on Mathematical Software (TOMS) : Volume 27
ACM Transactions on Mathematical Software (TOMS) : Volume 26
Issue 4, Dec 2000
Issue 3, Sept 2000
Issue 2(Special issue in honor of John Rice's 65th birthday), June 2000
Editorial: special issue in honor of John Rice's 65th birthday
John R. Rice: biographical and professional notes
PYTHIA-II: a knowledge/database system for managing performance data and recommending scientific software
Mining and visualizing recommendation spaces for elliptic PDEs with continuous attributes
Accurate approximate solution of partial differential equations at off-mesh points
How to vectorize the algebraic multilevel iteration
Algorithm 803: a simpler macro processor
Issue 1, March 2000
ACM Transactions on Mathematical Software (TOMS) : Volume 25
ACM Transactions on Mathematical Software (TOMS) : Volume 24
ACM Transactions on Mathematical Software (TOMS) : Volume 23
ACM Transactions on Mathematical Software (TOMS) : Volume 22
ACM Transactions on Mathematical Software (TOMS) : Volume 21
ACM Transactions on Mathematical Software (TOMS) : Volume 20
ACM Transactions on Mathematical Software (TOMS) : Volume 19
ACM Transactions on Mathematical Software (TOMS) : Volume 18
ACM Transactions on Mathematical Software (TOMS) : Volume 17
ACM Transactions on Mathematical Software (TOMS) : Volume 16
ACM Transactions on Mathematical Software (TOMS) : Volume 15
ACM Transactions on Mathematical Software (TOMS) : Volume 14
ACM Transactions on Mathematical Software (TOMS) : Volume 13
ACM Transactions on Mathematical Software (TOMS) : Volume 12
ACM Transactions on Mathematical Software (TOMS) : Volume 11
ACM Transactions on Mathematical Software (TOMS) : Volume 10
ACM Transactions on Mathematical Software (TOMS) : Volume 9
ACM Transactions on Mathematical Software (TOMS) : Volume 8
ACM Transactions on Mathematical Software (TOMS) : Volume 7
ACM Transactions on Mathematical Software (TOMS) : Volume 6
ACM Transactions on Mathematical Software (TOMS) : Volume 5
ACM Transactions on Mathematical Software (TOMS) : Volume 4
ACM Transactions on Mathematical Software (TOMS) : Volume 3
ACM Transactions on Mathematical Software (TOMS) : Volume 2
ACM Transactions on Mathematical Software (TOMS) : Volume 1

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How to vectorize the algebraic multilevel iteration

Content Provider ACM Digital Library
Author Grosz, Lutz
Copyright Year 2000
Abstract We consider the algebraic multilevel iteration (AMLI) for the solution of systems of linear equations as they arise form a finite-difference discretization on a rectangular grid. Key operation is the matrix-vector product, which can efficiently be executed on vector and parallel-vector computer architectures if the nonzero entries of the matrix are concentrated in a few diagonals. In order to maintain this structure for all matrices on all levels coarsening in alternating directions is used. In some cases it is necessary to introduce additional dummy grid hyperplanes. The data movements in the restriction and prolongation are crucial, as they produce massive memory conflicts on vector architectures. By using a simple performance model the best of the possible vectorization strategies is automatically selected at runtime. Examples show that on a Fujitsu VPP300 the presented implementation of AMLI reaches about 85% of the useful performance, and scalability with respect to computing time can be achieved.
Starting Page 293
Ending Page 309
Page Count 17
File Format PDF
ISSN 00983500
e-ISSN 15577295
DOI 10.1145/353474.353483
Volume Number 26
Issue Number 2
Journal ACM Transactions on Mathematical Software (TOMS)
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2000-06-01
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Large linear systems Multigrid method Numerical software Parallel processing Preconditioned iterative solver Vector computer
Content Type Text
Resource Type Article
Subject Applied Mathematics Software
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