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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 76
PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping and Z. Bittnar
Paper 44
Effectiveness of Approximate Inverse Preconditioning by using the MR algorithm on an Origin 2400 T. Tanaka and T. Nodera
Department of Mathematics, Keio University, Yokohama, Japan Full Bibliographic Reference for this paper
T. Tanaka, T. Nodera, "Effectiveness of Approximate Inverse Preconditioning by using the MR algorithm on an Origin 2400", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Third International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 44, 2002. doi:10.4203/ccp.76.44
Keywords: preconditioning, approximate inverses, minimal residual algorithm, threshold dropping strategies, sparse linear systems, GMRES algorithm.
Summary
We now consider the linear system of equations
where the coefficient matrix ![]()
where ![]() ![]() ![]() ![]() In recent papers, it has been shown that the direct computation of sparse approximate inverses leads to appropriate preconditioners in parallel environment. The starting point is the minimization problem for a given sparsity pattern of the matrix ![]() ![]() ![]() ![]() ![]() ![]() These procedures have originally been developed for fixed sparsity pattern of ![]() ![]() ![]()
We will analyze another way to determine
previously a suitable pattern for
Numerical experiments are given for solving the discretized problems
(44.1) derived from the boundary value problems of PDE (partial
differential equation) on the shared memory parallel
machine Origin 2400 with 8 processors.
For instance, several numerical results of
two dimensional convection diffusion problems will be reported in our
presentation.
We also present both from a theoretical and a practical point of view
that the preconditioner created by MR algorithm is useful
in improving the convergence of restarted GMRES( purchase the full-text of this paper (price £20)
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