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  • 1
    Electronic Resource
    Electronic Resource
    The block decomposition of a vandermonde matrix and its applications (1981)
    Springer
    BIT 21 (1981), S. 505-517 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a new algorithm for the solution of linear equations with a Vandermonde coefficient matrix. The algorithm can also be used to solve the dual problem. Since the algorithm uses a block decomposition of the matrix, it is especially suitable for parallel computation. A variation of the block decomposition leads to the efficient solution of the interpolation problem with complex-conjugate interpolation points where the coefficients of the interpolating polynomial are real. In addition the algorithm can be used to solve some kinds of confluent Vandermonde systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932847
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Preconditioned conjugate gradient methods for the incompressible Navier-Stokes equations (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 273-295 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; ILU(l) ; Preconditioned conjugate gradient ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A robust technique for solving primitive variable formulations of the incompressible Navier-Stokes equations is to use Newton iteration for the fully implicit non-linear equations. A direct sparse matrix method can be used to solve the Jacobian but is costly for large problems; an alternative is to use an iterative matrix method. This paper investigates effective ways of using a conjugate-gradient-type method with an incomplete LU factorization preconditioner for two-dimensional incompressible viscous flow problems. Special attention is paid to the ordering of unknowns, with emphasis on a minimum updating matrix (MUM) ordering. Numerical results are given for several test problems.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150303
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  • 3
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    Wavelet Sparse Approximate Inverse Preconditioners (1996)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.
    Keywords: Numerical Analysis
    Type: NASA-CR-203272 , NAS 1.26:203272 , RIACS-TR-96-18
    Format: application/pdf
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  • 4
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    A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid (1995)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.
    Keywords: Fluid Mechanics and Heat Transfer
    Type: NASA-CR-201051 , NAS 1.26:201051 , RIACS-TR-95-07
    Format: application/pdf
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