Journal of the Korean Society for Industrial and Applied Mathematics
- Volume 5 Issue 1
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- Pages.85-100
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- 2001
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- 1226-9433(pISSN)
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- 1229-0645(eISSN)
A Robust Preconditioner on the CRAY-T3E for Large Nonsymmetric Sparse Linear Systems
- Ma, Sangback (Department of Computer science Hanyang University) ;
- Cho, Jaeyoung (Department of Computer science Hanyang University)
- Published : 2001.06.30
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. Finally, due to the blocking effect, it will be effective for ill-conditioned problems. 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, and for an ill-conditioned matrix from the shell problem from the Harwell-Boeing collection. CRAY-T3E with 128 nodes was used. MPI library was used for interprocess communications. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices and for the shell problem only the Multi-Color Block SOR converges.
Keywords