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IMA Journal of Numerical Analysis 2001 21(1):265-283; doi:10.1093/imanum/21.1.265
© 2001 by Institute of Mathematics and its Applications
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An additive Schwarz method for the h-p version of the boundary element method for hypersingular integral equations in R3

Norbert Heuer1 and Ernst P. Stephan2

1 Institut für Wissenschaftliche Datenverarbeitung, Universität Bremen, Postfach 33 04 40, 28334 Bremen, Germany 2 Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany

We study a preconditioner for the h-p version of the boundary element method for hypersingular integral equations in three dimensions. The preconditioner is based on a three-level decomposition of the underlying ansatz space, the levels being piecewise bilinear functions on a coarse grid, piecewise bilinear functions on a fine grid, and piecewise polynomials of high degree on the fine grid. We prove that the condition number of the preconditioned linear system is bounded by maxj (1 + log Hjpj/hj)2 where Hj is the diameter of an element {Gamma}j of the coarse grid, hj is the size of the elements of the fine grid on {Gamma}j, and pj is the maximum of the polynomial degrees used in {Gamma}j. Numerical results supporting our theory are reported.

Received 9 March 1999. Accepted 19 July 1999.


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