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Excessive Over-Relaxation Method for Multigrid Poisson Solvers

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Abstract

The class of numerical solvers know as Multigrid methods have become more popular in recent years, due to the falling price of memory and their improved performance over conventional differential equation solvers. In this paper we present a modification of the standard multigrid method that results in an improvement in performance of up to 40% in the solution of Poisson like equations. The inclusion of Successive Over-Relaxation (SOR) as a smoothing operator in the multigrid algorithm has generally been considered detrimental to the performance of Multigrid since it introduces spurious error frequency components. We show that, if due care is taken in the implementation, the inclusion of SOR in multigrid is desirable and can result in optimum over-relaxation coefficients outside the range determined by conventional convergence theory.

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Authors and Affiliations

  1. Device Modelling Group, Department of Electronics and Electrical Engineering, Glasgow University, Rankine Building, Oakfield Avenue, Glasgow, G12 8LT, UK

    C. Millar, A. Asenov & J.R. Watling

Authors
  1. C. Millar
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  2. A. Asenov
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  3. J.R. Watling
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Millar, C., Asenov, A. & Watling, J. Excessive Over-Relaxation Method for Multigrid Poisson Solvers. Journal of Computational Electronics 1, 341–345 (2002). https://doi.org/10.1023/A:1020791306305

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  • DOI: https://doi.org/10.1023/A:1020791306305

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