Two-Level Additive Schwarz Preconditioners for the h-p Version of the Galerkin Boundary Element Method for 2-d Problems |
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Authors: | T Tran E P Stephan |
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Affiliation: | (1) School of Mathematical Sciences The Australian National University Present address: School of Computing and Mathematics Deakin University 662 Blackburn Road Clayton, VIC 3168, Australia e-mail: thanh@deakin.edu.au, AU;(2) Institut für Angewandte Mathematik University of Hannover Welfengarten 1 30167 Hannover, Germany e-mail: stephan@ifam.uni-hannover.de, DE |
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Abstract: | We study two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method when used to solve hypersingular integral equations of the first kind, which
arise from the Neumann problems for the Laplacian in two dimensions. Overlapping and non-overlapping methods are considered.
We prove that the non-overlapping preconditioner yields a system of equations having a condition number bounded by where H
i
is the length of the i-th subdomain, h
i
is the maximum length of the elements in this subdomain, and p is the maximum polynomial degree used. For the overlapping method, we prove that the condition number is bounded by where δ is the size of the overlap and H=max
i
H
i
. We also discuss the use of the non-overlapping method when the mesh is geometrically graded. The condition number in that
case is bounded by clog2
M, where M is the degrees of freedom.
Received October 27, 2000, revised March 26, 2001 |
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Keywords: | AMS Subject Classifications: 65N55 65N38 |
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