Parallel Preconditioning of Iterative Solvers by Factorized Sparse Approximate Inverse Preconditioners
Miroslav Tuma(CERFACS, Parallel Algorithms Project)
Wednesday December 9, 11.00 a.m CERFACS Conference Room
Abstract :
We consider the solution of sparse linear systems $Ax = b$ by preconditioned iterative methods. One of the key problems in this field is to find such preconditioners which are cheap to compute, fairly robust, easy to apply on high performance architectures and which would deliver good convergence rates when coupled with an appropriate iterative method. In this contribution we will concentrate on factorized sparse approximate inverse preconditioners based on the AINV algorithm (M. Benzi, C.D. Meyer and M. Tuma, 1996, 1998). Using graph partitioning we are able to parallelize the calculation of the preconditioner, resulting in a fully parallel approach.
The algorithm has been implemented on the ASCI Blue Mountain cluster of SGI/Origin 2000 parallel systems at Los Alamos. The code is being used to solve linear systems of order up to a few millions from several applications. Numerical experiments will be presented to illustrate the excellent scalability behavior of the algorithm.
This is a joint work with Michele Benzi, Los Alamos National Laboratory and Jose Marin, Polytechnic University of Valencia.
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