A parallel version of QMRCGSTAB method for large linear systems in distributed parallel environments

In this paper, a parallel QMRCGSTAB method (PQMRCGSTAB method) for solving large sparse linear systems with unsymmetrical coefficient matrices is proposed for distributed parallel environments. The method reduces four global synchronization points to one by reconstructing QMRCGSTAB method. It combines the elements of numerical stability with the characters of design of parallel algorithms. The cost is only a little increased computation. Performance analysis shows that PQMRCGSTAB method has better parallelism and scalability than QMRCGSTAB method. Numerical experiments show the effectiveness of our method.