A Scalable Parallel Preconditioner on the CRAY - T3E for Large Nonsymmetric Sparse Linear Systems


The KIPS Transactions:PartA, Vol. 8, No. 3, pp. 227-234, Sep. 2001
10.3745/KIPSTA.2001.8.3.227,   PDF Download:

Abstract

In this paper we propose a block-type parallel preconditioner for solving large sparse nonsymmetric linear systems, which we expect to be scalable. It is Multi-Color Block SOR preconditioner, combined with direct sparse matrix solver. For the Laplacian matrix the SOR method is known to have a nondeteriorating rate of convergence when used with Multi-Color ordering. Since most of the time is spent on the diagonal inversion, which is done on each processor, we expect it to be a good scalable preconditioner. We compared it with four other preconditioners, which are ILU(0)-wavefront ordering, ILU(0)-Multi-Color ordering, SPAI (SParse Approximate Inverse), and SSOR preconditioner. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 1024 x 1024. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR is scalable and gives the best performances.


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Cite this article
[IEEE Style]
S. B. Ma, "A Scalable Parallel Preconditioner on the CRAY - T3E for Large Nonsymmetric Sparse Linear Systems," The KIPS Transactions:PartA, vol. 8, no. 3, pp. 227-234, 2001. DOI: 10.3745/KIPSTA.2001.8.3.227.

[ACM Style]
Sang Back Ma. 2001. A Scalable Parallel Preconditioner on the CRAY - T3E for Large Nonsymmetric Sparse Linear Systems. The KIPS Transactions:PartA, 8, 3, (2001), 227-234. DOI: 10.3745/KIPSTA.2001.8.3.227.