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Domain decomposition and parallel processing of a finite element model of the shallow water equations. (English) Zbl 0784.76052
Summary: We present nonoverlapping domain decomposition techniques applied to a two-stage Numerov-Galerkin finite element model of the shallow water equations over a limited-area domain. The Schur complement matrix formulation is employed and a modified interface matrix approach is proposed to handle the coupling between subdomains. The resulting nonsymmetric Schur complement matrices, modified interface matrices as well as the subdomain coefficient matrices are solved using preconditioned conjugate gradient squared non-symmetric iterative solvers. Various stages of the finite element solution are parallelized and the code is implemented on a four processor CRAY Y-MP supercomputer applying multitasking techniques in a dedicated environment.

76M10 Finite element methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
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