On the acceleration of the preconditioned simultaneous displacement method

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Abstract

This paper considers the application of various accelerated techniques of the Preconditioned Simultaneous Displacement method (PSD method) [3]. The resulting methods possess rates of convergence which are improved by an order of magnitude as compared with the well known SOR method. However, it is shown that the PSD-Variable Extrapolation method (PSD-VE method) combined with a computational work reduction scheme [10] seems to offer a substantial saving in overall efficiency. The application of the analysis to the model problem involving Laplace's equation and the generalised Dirichlet problem is considered. In addition, the results of a number of various numerical experiments are also given. It is concluded that the PSD-VE method with Niethammer's approach is superior than SOR at least for the cases considered.

References (20)

  • D.J. Evans et al.

    The preconditioned simultaneous displacement method

    Math. Comp. Sim.

    (1980)
  • V.I. Lebedev et al.

    Ordering of the iterative parameters in the cyclical Chebyshev iterative method

    Zh. Vychislit. Mat. Fiz.

    (1971)
  • D.M. Young

    On the accelerated SSOR method for solving large linear systems

    Advances in Mathematics

    (1977)
  • D.J. Evans

    The use of preconditioning in iterative methods for solving linear equations with symmetric positive definite matrices

    J. Inst. Math. Applics.

    (1968)
  • D.J. Evans

    Comparison of the convergence rates of iterative methods for solving linear equations with preconditioning

  • G.H. Golub et al.

    Chebyshev semi-iterative methods, successive over-relaxation iterative methods and second order Richardson iterative methods

    Numer. Math.

    (1961)
  • M.R. Hestenes et al.

    Method of conjugate gradients for solving linear systems

    J. Res. Nat. Bur. Standards

    (1952)
  • N.M. Missirlis

    Preconditioned iterative methods for solving elliptic partial differential equations

  • N.M. Missirlis et al.

    On the convergence of some generalised preconditioned iterative methods

    SINUM

    (1981)
  • N.M. Missirlis et al.

    The extrapolated successive overrelaxation method (ESOR method), for consistently ordered matrices

    (1979)
There are more references available in the full text version of this article.

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