MPI Management of Hermite Collocation Computation on a Distributed-Shared Memory System

The organization and management of the intense computation involved in the solution of large, sparse and non-symmetric systems of equations, arising from the discretization of Elliptic Boundary Value Problems (BVPs) by the Hermite Collocation method, on a Distributed-Shared Memory (DSM) multiprocessor environment is the problem considered herein. As the size of the problem directly suggests the usage of iterative methods, we consider the parallel implementation of the Successive Over-Relaxation (SOR) and the preconditioned Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) methods on DSM systems. Using the parallel algorithms we devised in [9, 10], which take advantage of the red-black structure of the Collocation matrix, we address the problem of efficiently managing the whole computation, through the MPI programming model, on a DSM system. The application was developed on a SGI Origin 350 DSM multiprocessor computer and its performance is revealed by the speedup measurements included. Key-Words : Collocation, SOR, preconditioned Bi-CGSTAB, Red-Black Orderings, MPI, DSM Systems.