How fast the laplace equation was solved in 1995

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Abstract

On the occasion of the third centenary of the appointment of Johann Bernoulli at the University of Groningen, a number of linear systems solvers for some Laplace-like equations have been compared during a one-day workshop. CPU times of several advanced solvers measured on the same computer (an HP-755 workstation) are presented, which makes it possible to draw clear conclusions about the performance of these solvers.

References (29)

  • H.A. van der Vorst

    ICCG and related methods for 3D problems on vector computers

    Comput. Phys. Comm.

    (1989)
  • P.M. de Zeeuw

    Matrix-dependent prolongations and restrictions in a blackbox multi-grid solver

    J. Comput. Appl. Math.

    (1990)
  • O. Axelsson et al.

    The nested recursive two level factorization for nine-point difference matrices

    SIAM J. Sci. Statist. Comput.

    (1991)
  • O. Axelsson et al.

    On the eigenvalue distribution of a class of preconditioning methods

    Numer. Math.

    (1986)
  • E.F.F. Botta et al.

    Preconditioning techniques for matrices with arbitrary sparsity patterns

  • E.F.F. Botta et al.

    The convergence behaviour of iterative methods on severely stretched grids

    Internat. J. Numer. Methods Engrg.

    (1993)
  • C.W. Brand

    An incomplete-factorization preconditioning using red-black ordering

    Numer. Math.

    (1992)
  • B. Buzbee et al.

    On direct methods for solving Poisson's equation

    SIAM J. Numer. Anal.

    (1970)
  • T.A. Davis et al.

    A combined unifrontal/multifrontal method for unsymmetric sparse matrices

  • K. Dekker

    Preconditioned conjugate gradient techniques for the solution of time-dependent differential equations

  • J.W. Demmel et al.

    A supernodal approach to sparse partial pivoting

  • S.C. Eisenstat

    Efficient implementation of a class of preconditioned conjugate gradient methods

    SIAM J. Sci. Statist. Comput.

    (1981)
  • I. Gustafsson

    A class of first order factorization methods

    BIT

    (1978)
  • J.A. Meijerink et al.

    An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix

    Math. Comp.

    (1977)
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