Efficient ICCG on a Shared Memory Multiprocessor

In this paper we discuss different approaches for exploiting parallelism in the ICCG method for solving large sparse symmetric positive definite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector products are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are representative of a large class of problems solved using iterative methods are used. We show that a static analysis to determine data dependences in the triangular solve can greatly improve its parallel efficiency. We also show that, under certain circumstances, ignoring symmetry and storing all nonzero elements of a sparse matrix can reduce solution time substantially.