Additive Schwarz algorithms for the p version of the Galerkin boundary element method |
| |
Authors: | Thanh Tran Ernst P Stephan |
| |
Institution: | (1) School of Mathematics, University of New South Wales, Sydney 2052, Australia, AU;(2) Institut für Angewandte Mathematik, University of Hannover, Welfengarten 1, 30167 Hannover, Germany; e-mail: stephan@ifam.uni-hannover.de, DE |
| |
Abstract: | Summary. We study some additive Schwarz algorithms for the version Galerkin boundary element method applied to some weakly singular and hypersingular integral equations of the first
kind. Both non-overlapping and overlapping methods are considered. We prove that the condition numbers of the additive Schwarz
operators grow at most as independently of h, where p is the degree of the polynomials used in the Galerkin boundary element schemes and h is the mesh size. Thus we show that additive Schwarz methods, which were originally designed for finite element discretisation
of differential equations, are also efficient preconditioners for some boundary integral operators, which are non-local operators.
Received June 15, 1997 / Revised version received July 7, 1998 / Published online February 17, 2000 |
| |
Keywords: | Mathematics Subject Classification (1991): 65N55 65N38 |
本文献已被 SpringerLink 等数据库收录! |
|