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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board Member: Axelsson, Owe / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Pironneau, O. / Quarteroni, Alfio / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Widlund, O. / Zou, Jun

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An overlapping additive Schwarz preconditioner for boundary element approximations to the Laplace screen and Lamé crack problems

T. Tran / E.P. Stephan

School of Mathematics, University of New South Wales, Sydney 2052, Australia

Institut für Angewandte Mathematik, University of Hannover, 30167 Hannover, Germany

Citation Information: Journal of Numerical Mathematics jnma. Volume 12, Issue 4, Pages 311–330, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: 10.1515/1569395042571265, November 2004

We study a two-level overlapping additive Schwarz preconditioner for the h-version of the Galerkin boundary element method when used to solve hypersingular integral equations of the first kind on an open surface in These integral equations result from Neumann problems for the Laplace and Lamé equations in the exterior of the surface. We prove that the condition number of the preconditioned system is bounded by O(1 + log2(H/δ)), where H denotes the diameter of the subdomains and δ the size of the overlap.

Key Words: Galerkin boundary element method,; h version,; additive Schwarz,; overlapping,; preconditioned conjugate gradient

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