IJPAM: Volume 12, No. 1 (2004)

A MULTIPLICATIVE SCHWARZ ALGORITHM FOR
THE GALERKIN BOUNDARY ELEMENT
APPROXIMATION OF THE WEAKLY SINGULAR
INTEGRAL OPERATOR IN THREE DIMENSIONS

Matthias Maischak$^1$, Ernst P. Stephan$^2$, Thanh Tran$^3$
$^{1,2}$Institut of Applied Mathematics
University of Hannover
30167 Hannover, GERMANY
$^1$e-mail: maischak@ifam.uni-hannover.de
$^2$e-mail: stephan@ifam.uni-hannover.de
$^3$School of Mathematics
University of New South Wales
Sydney 2052, AUSTRALIA
e-mail: t.tran@maths.unsw.edu.au


Abstract.We study a multiplicative Schwarz method for the $h$-version Galerkin boundary element method for a weakly singular integral equation of the first kind in 3 dimensions. We prove a bound for the contraction rate of the multiplicative Schwarz operator which depends on the quotient $n_H=H/h$ of the mesh sizes $H$ and $h$ of the coarse grid space and the fine grid space, respectively. The boundary element space consists of piecewise constant functions on surface meshes. Computational results are presented which support our theory.

Received: April 7, 2003

AMS Subject Classification: 65N55, 65N38

Key Words and Phrases: Galerkin boundary element method, weakly singular integral equations, multiplicative Schwarz, domain decomposition

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 1