Advances in Computational Mathematics

, Volume 7, Issue 1–2, pp 135–156 | Cite as

Remarks on the optimal convolution kernel for CSOR waveform relaxation

  • Min Hu
  • Ken Jackson
  • Jan Janssen
  • Stefan Vandewalle


The convolution SOR waveform relaxation method is a numerical method for solving large-scale systems of ordinary differential equations on parallel computers. It is similar in spirit to the SOR acceleration method for solving linear systems of algebraic equations, but replaces the multiplication with an overrelaxation parameter by a convolution with a time-dependent overrelaxation function. Its convergence depends strongly on the particular choice of this function. In this paper, an analytic expression is presented for the optimal continuous-time convolution kernel and its relation to the optimal kernel for the discrete-time iteration is derived. We investigate whether this analytic expression can be used in actual computations. Also, the validity of the formulae that are currently used to determine the optimal continuous-time and discrete-time kernels is extended towards a larger class of ODE systems.

convolution, iterative methods, parallel ODE solvers, successive overrelaxation, waveform relaxation. 


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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Min Hu
  • Ken Jackson
  • Jan Janssen
  • Stefan Vandewalle

There are no affiliations available

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