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On the convergence of the multigrid method for a hypersingular integral equation of the first kind

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Summary

We present a multigrid method to solve linear systems arising from Galerkin schemes for a hypersingular boundary integral equation governing three dimensional Neumann problems for the Laplacian. Our algorithm uses damped Jacobi iteration, Gauss-Seidel iteration or SOR as preand post-smoothers. If the integral equation holds on a closed, Lipschitz surface we prove convergence ofV- andW-cycles with any number of smoothing steps. If the integral equation holds on an open, Lipschitz surface (covering crack problems) we show convergence of theW-cycle. Numerical experiments are given which underline the theoretical results.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, D-6100, Darmstadt, Federal Republic of Germany

    T. von Petersdorff

  2. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA

    E. P. Stephan

Authors
  1. T. von Petersdorff
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  2. E. P. Stephan
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von Petersdorff, T., Stephan, E.P. On the convergence of the multigrid method for a hypersingular integral equation of the first kind. Numer. Math. 57, 379–391 (1990). https://doi.org/10.1007/BF01386417

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  • DOI: https://doi.org/10.1007/BF01386417

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