Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment

Kenji Ono, Yasuhiro Kawashima

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Elliptic partial difference equations like Poisson's equation are used in many fields of application. However, the coefficientmatrix of the derived algebraic equation is large and sparse, and so its inversion is expensive. Various iterative methods are used to solve such a sparse matrix system. Although there have been many studies on solving the large sparse matrix system [1, 2, 3, 4, 5, 6, 7], there have been few reports on the implementation and performance of the iterative method with multicolor ordering. In this paper, a novel implementation technique to enhance the performance of the 2-colored SOR method is proposed, which eliminates the recursion for the standard 7-point stencil on the Cartesian grid in three dimensions. The performance of the multicolor SOR method is investigated on both a shared memory vector/parallel computer and a symmetric multiprocessor machine in a distributed memory environment.

Original languageEnglish
Title of host publicationParallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications
Pages183-191
Number of pages9
DOIs
Publication statusPublished - Jan 1 2011
Event20th International Series of Meetings on Parallel Computational Fluid Dynamics, CFD 2008 - Lyon, France
Duration: May 19 2008May 22 2008

Publication series

NameLecture Notes in Computational Science and Engineering
Volume74 LNCSE
ISSN (Print)1439-7358

Other

Other20th International Series of Meetings on Parallel Computational Fluid Dynamics, CFD 2008
CountryFrance
CityLyon
Period5/19/085/22/08

Fingerprint

SOR Method
Distributed Memory
Shared Memory
Iterative methods
Consecutive
Sparse matrix
Data storage equipment
Poisson equation
Difference equations
Vector Computer
Iteration
Partial Difference Equations
Cartesian Grid
Parallel Computers
Multiprocessor
Poisson's equation
Recursion
Algebraic Equation
Three-dimension
Inversion

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Cite this

Ono, K., & Kawashima, Y. (2011). Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment. In Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications (pp. 183-191). (Lecture Notes in Computational Science and Engineering; Vol. 74 LNCSE). https://doi.org/10.1007/978-3-642-14438-7_19

Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment. / Ono, Kenji; Kawashima, Yasuhiro.

Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications. 2011. p. 183-191 (Lecture Notes in Computational Science and Engineering; Vol. 74 LNCSE).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ono, K & Kawashima, Y 2011, Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment. in Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications. Lecture Notes in Computational Science and Engineering, vol. 74 LNCSE, pp. 183-191, 20th International Series of Meetings on Parallel Computational Fluid Dynamics, CFD 2008, Lyon, France, 5/19/08. https://doi.org/10.1007/978-3-642-14438-7_19
Ono K, Kawashima Y. Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment. In Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications. 2011. p. 183-191. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-642-14438-7_19
Ono, Kenji ; Kawashima, Yasuhiro. / Multicolor SOR method with consecutive memory access implementation in a shared and distributed memory parallel environment. Parallel Computational Fluid Dynamics 2008 - Parallel Numerical Methods, Software Development and Applications. 2011. pp. 183-191 (Lecture Notes in Computational Science and Engineering).
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