Parallelization of ILU decomposition for elliptic boundary value problem of the PDE on AP3000

Kentaro Moriya, Takashi Nodera

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

1 Citation (Scopus)

Abstract

ILU (or Incomplete LU) decomposition is one of the most popular preconditioners for large and sparse linear systems of equations. However, it is difficult to implement the ILU preconditioner on distributed memory parallel computers, because the process consists of forward and backward substitution. The block divided method is one of the algorithms that can paralletize the ILU preconditioner for the linear system obtained by applying the finite difference method to discretize the elliptic boundary value problem of the PDE (or partial differential equation). However, on a distributed memory parallel computer, since the communication overhead is significantly large, the ILU preconditioner does not perform well. We propose an algorithm that decreases the communication overhead on the block divided method and determines the appropriate band-size. Based on our approach, the BiCGStab(g) method with the ILU preconditioner is implemented on the distributed memory parallel computer, Fujitsu AP3000. We also analyze the performance of parallelism in the operation of the ILU preconditioner through numerical results.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages344-353
Number of pages10
Volume1615
ISBN (Print)3540659692, 9783540659693
DOIs
Publication statusPublished - 1999
Event2nd International Symposium on High Performance Computing, ISHPC 1999 - Kyoto, Japan
Duration: 1999 May 261999 May 28

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1615
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other2nd International Symposium on High Performance Computing, ISHPC 1999
CountryJapan
CityKyoto
Period99/5/2699/5/28

Fingerprint

LU decomposition
Elliptic Boundary Value Problems
Parallelization
Preconditioner
Boundary value problems
Partial differential equations
Partial differential equation
Decomposition
Data storage equipment
Linear systems
Distributed Memory
Parallel Computers
Communication
Finite difference method
Substitution reactions
Sparse Linear Systems
Linear system of equations
Difference Method
Parallelism
Substitution

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Moriya, K., & Nodera, T. (1999). Parallelization of ILU decomposition for elliptic boundary value problem of the PDE on AP3000. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1615, pp. 344-353). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1615). Springer Verlag. https://doi.org/10.1007/BFb0094936

Parallelization of ILU decomposition for elliptic boundary value problem of the PDE on AP3000. / Moriya, Kentaro; Nodera, Takashi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1615 Springer Verlag, 1999. p. 344-353 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1615).

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

Moriya, K & Nodera, T 1999, Parallelization of ILU decomposition for elliptic boundary value problem of the PDE on AP3000. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1615, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1615, Springer Verlag, pp. 344-353, 2nd International Symposium on High Performance Computing, ISHPC 1999, Kyoto, Japan, 99/5/26. https://doi.org/10.1007/BFb0094936
Moriya K, Nodera T. Parallelization of ILU decomposition for elliptic boundary value problem of the PDE on AP3000. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1615. Springer Verlag. 1999. p. 344-353. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/BFb0094936
Moriya, Kentaro ; Nodera, Takashi. / Parallelization of ILU decomposition for elliptic boundary value problem of the PDE on AP3000. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1615 Springer Verlag, 1999. pp. 344-353 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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