Abstract
A unified framework is presented for a fully parallel solution of large, sparse nonsymmetric linear systems on distributed memory multiprocessors. Unlike earlier work, both symbolic and numeric steps are parallelized. Parallel Cartesian nested dissection is used to compute a fill-reducing ordering of A using a compact representation of the column intersection graph, and the resulting separator tree is used to estimate the structure of the factor and to distribute data and perform multifrontal numeric computations. When the matrix is nonsymmetric but square, the numeric computations involve Gaussian elimination with partial pivoting; when the matrix is overdetermined, row-oriented Householder transforms are applied to compute the triangular factor of an orthogonal factorization. Extensive empirical results are provided to demonstrate that the approach is effective both in preserving sparsity and achieving good parallel performance on an Intel iPSC/860.
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