PARALLEL BLOCK PRECONDITIONING TECHNIQUES FOR THE NUMERICAL-SIMULATION OF THE SHALLOW-WATER FLOW USING FINITE-ELEMENT METHODS

In this paper, we report our work on applying Krylov iterative methods, accelerated by parallelizable domain-decomposed (DD) preconditioners, to the solution of nonsymmetric linear algebraic equations arising from implicit time discretization of a finite element model of the shallow water equations on a limited-area domain. Two types of previously proposed DD preconditioners are employed and a novel one is advocated to accelerate, with post-preconditioning, the convergence of three popular and competitive Krylov iterative linear solvers. Performance sensitivities of these preconditioners to inexact subdomain solvers are also reported. Autotasking, the parallel processing capability representing the third phase of multitasking libraries on GRAY Y-MP, has been exploited and successfully applied to both loop and subroutine level parallelization. Satisfactory speedup results were obtained. On the other hand, automatic loop-level parallelization, made possible by the autotasking preprocessor, attained only a speedup smaller than a factor of two. (C) 1995 Academic Press, Inc.