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Using a finite difference method to discretize a two dimensional elliptic boundary value problem, we obtain systems of linear equations Ax=b, where the coefficient matrix A is a large, sparse, and nonsingular. These systems are often solved by preconditioned iterative methods. This paper presents a data distribution and a communication scheme for the parallelization of the preconditioner based on the incomplete LU factorization. At last, parallel performance tests of the preconditioner, using BiCGStab(ℓ) and GMRES(m) method, are carried out on a distributed memory parallel machine AP1000. The numerical results show that the preconditioner based on the incomplete LU factorization can be used even for MIMD parallel machines.

The parallelization of the incomplete LU factorization on AP1000