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A Parallel Implementation Of The BlockPartitioned Inverse Multifrontal Zsparse Algorithm
, 1995
"... . The sparse inverse subset problem is the computation of the entries of the inverse of a sparse matrix for which the corresponding entry is nonzero in the factors of the matrix. We present a parallel, blockpartitioned formulation of the inverse multifrontal algorithm to compute the sparse inverse ..."
Abstract

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. The sparse inverse subset problem is the computation of the entries of the inverse of a sparse matrix for which the corresponding entry is nonzero in the factors of the matrix. We present a parallel, blockpartitioned formulation of the inverse multifrontal algorithm to compute the sparse inverse subset. Numerical results for an implementation of this algorithm on an 8processor, sharedmemory CrayC98 architecture are discussed. We show that for large problems we obtain efficiency ratings of over 80% and performance in excess of 1 Gflop. 1. Introduction. An efficient method to compute the sparse inverse subset (Zsparse) is important in practical applications such as the computation of short circuit currents in power systems or in estimating the variances of the fitted parameters in the leastsquared datafitting problem. (The sparse inverse subset (Zsparse), is defined as the set of inverse entries in locations corresponding to the positions of nonzero entries in the LDU factorize...
Computing the Sparse Inverse . . .
, 1995
"... We present the symmetric inverse multifrontal method for computing the sparse inverse subset of symmetric matrices. The symmetric inverse multifrontal approach uses an equation presented by Takahashi, Fagan, and Chin to compute the numerical values of the entries of the inverse, and an inverted form ..."
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We present the symmetric inverse multifrontal method for computing the sparse inverse subset of symmetric matrices. The symmetric inverse multifrontal approach uses an equation presented by Takahashi, Fagan, and Chin to compute the numerical values of the entries of the inverse, and an inverted form of the symmetric multifrontal method of Duff and Reid to guide the computation. We take advantage of related structures that allow the use of dense matrix kernels (levels 2 & 3 BLAS) in the computation of this subset. We discuss the theoretical basis for this new algorithm and give numerical results for a serial implementation and demonstrate its performance on a CrayC98.
TWO ELEMENTBYELEMENT ITERATIVE SOLUTIONS FOR SHALLOW WATER EQUATIONS ∗
"... Abstract. In this paper we apply the generalized Taylor–Galerkin finite element model to simulate bore wave propagation in a domain of two dimensions. For stability and accuracy reasons, we generalize the model through the introduction of four free parameters. One set of parameters is rigorously det ..."
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Abstract. In this paper we apply the generalized Taylor–Galerkin finite element model to simulate bore wave propagation in a domain of two dimensions. For stability and accuracy reasons, we generalize the model through the introduction of four free parameters. One set of parameters is rigorously determined to obtain the highorder finite element solution. The other set of free parameters is determined from the underlying discrete maximum principle to obtain the monotonic solutions. The resulting two models are used in combination through the flux correct transport technique of Zalesak, thereby constructing a finite element model which has the ability to capture hydraulic discontinuities. In addition, this paper highlights the implementation of two Krylov subspace iterative solvers, namely, the biconjugate gradient stabilized (BiCGSTAB) and the generalized minimum residual (GMRES) methods. For the sake of comparison, the multifrontal direct solver is also considered. The performance characteristics of the investigated solvers are assessed using results of a standard test widely used as a benchmark in hydraulic modeling. Based on numerical results, it is shown that the present finite element method can render the technique suitable for solving shallow water equations with sharply varying solution profiles. Also, the GMRES solver is shown to have a much better convergence rate than the BiCGSTAB solver, thereby saving much computing time compared to the multifrontal solver. Key words. Taylor–Galerkin finite element model, discrete maximum principle, flux correct transport technique, BiCGSTAB, GMRES, multifrontal direct solver, sharply varying