A new successive relaxation scheme for the W-matrix solution method on a shared memory parallel computer

The W-matrix method has the potential to be efficient for parallel computing as a substitute for the precedence stringent substitution schemes, which are being commonly used on sequential computers for the solution of sparse linear matrix equations, with the support of appropriate reordering and partitioning algorithms. In this paper, the factors which may affect the performance of the W-matrix method are examined first. A bus reordering and partitioning scheme is then proposed which is aimed at reducing the fill-ins in both the triangular matrices L and U and the W-matrices and adjusting the patterns of the W-matrices for better parallel efficiency. Tests conducted on a shared memory parallel computer proved the effectiveness of the proposed algorithm for various systems. Test results are presented and discussed,