Implementation of Iterative Methods for Large Sparse Nonsymmetric Linear Systems On a Parallel Vector Machine

Abstract

We restructure three outstanding iterative methods for large sparse nonsymmetric linear systems. These methods are CGS (conjugate gradient squared), CRS (conjugate residual squared), and Orthomin(k). The re structured methods are more suitable for vector and parallel processing. We implemented these methods on a parallel vector system. The linear systems for the nu merical tests are obtained from discretizing four two- dimensional elliptic partial differential equations by finite difference and finite element methods. A vectorizable and parallelizable version of incomplete LU precondi tioning is used. We restructured the subroutines to en hance the data locality in vector machines with storage hierarchy. Speedup was measured for multitasking by four processors.