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Parallel iterative computational methods for 3D finite element flow simulations. (English) Zbl 0952.76036

Summary: We discuss sparse matrix computational method and their parallel implementations for evaluating matrix-vector products in iterative solutions of coupled nonlinear equations encountered in finite elements flow simulations. Based on sparse computation schemes, we introduce globally-defined preconditioners by mixing clustered element-by-element preconditioning concept with incomplete factorization methods. These preconditioners are implemented on a CRAY T3D parallel supercomputer. In addition, the sparse schemes discussed here are applied to three-dimensional simulation of incompressible flow past a circular cylinder.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65F50 Computational methods for sparse matrices
65Y05 Parallel numerical computation
65H10 Numerical computation of solutions to systems of equations
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