On the convergence of the multigrid method for a hypersingular integral equation of the first kind |
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Authors: | T von Petersdorff E P Stephan |
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Institution: | (1) Fachbereich Mathematik, Technische Hochschule Darmstadt, D-6100 Darmstadt, Federal Republic of Germany;(2) School of Mathematics, Georgia Institute of Technology, 30332 Atlanta, GA, USA |
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Abstract: | 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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Keywords: | AMS(MOS): 65F10 65N30 45L10 CR: G1 9 |
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