COMPARISONS OF THE PARALLEL PRECONDITIONERS FOR LARGE NONSYMMETRIC SPARSE LINEAR SYSTEMS ON A PARALLEL COMPUTER

SANGBACK MA
2004 International journal of high speed computing  
In this paper we compare various parallel preconditioners for solving large sparse nonsymmetric linear systems. They are Point-SSOR, ILU(0) in the wavefront order, ILU(0) in the multi-color order, and Multi-Color Block SOR. The Point-SSOR is well-known, and ILU(0) is a one of the most popular preconditioner, but it is inherently serial. ILU(0) in the wavefront order maximizes the parallelism in the nutural order, and ILU(0) in the multi-color order s a simple way of achieving a parallelism of
more » ... der(N ), where N is the order of the matrix, but its convergence rate often deteriorates. Finally, we implemented the 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. Experiments were conducted for the Finite Difference discretizations of two problems with various meshsizes varying up to 2048 x 2048. The results show that Multi-Color Block SOR and ILU(0) with Multi-Color ordering give the best performances for the finite difference matrices.
doi:10.1142/s0129053304000232 fatcat:d33bmydqhvavdknmkzcmktp5vq