TY - GEN
T1 - Parallelization of ILU decomposition for elliptic boundary value problem of the PDE on AP3000
AU - Moriya, Kentaro
AU - Nodera, Takashi
N1 - Publisher Copyright:
© 1999, Springer-Verlag. All rights reserved.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
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U2 - 10.1007/BFb0094936
DO - 10.1007/BFb0094936
M3 - Conference contribution
AN - SCOPUS:84958051293
SN - 3540659692
SN - 9783540659693
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 344
EP - 353
BT - High Performance Computing - 2nd International Symposium, ISHPC 1999, Proceedings
A2 - Joe, Kazuki
A2 - Fukuda, Akira
A2 - Polychronopoulos, Constantine
A2 - Tomita, Shinji
PB - Springer Verlag
T2 - 2nd International Symposium on High Performance Computing, ISHPC 1999
Y2 - 26 May 1999 through 28 May 1999
ER -