Sonderforschungsbereich 393
	Preprint 7 / 2003

Harbrecht, Helmut ; Schneider, Reinhold : Wavelet based fast solution of boundary integral equations

Author(s):

Harbrecht, Helmut
Schneider, Reinhold

Title:

Wavelet based fast solution of boundary integral equations

Electronic source:

application/pdf
application/postscript

Preprint series:

Technische Universität Chemnitz, SFB 393 (Germany), SFB393-Preprint 7, 2003

Mathematics Subject Classification:

65N38			[ Boundary element methods ]
47A20			[ Dilations, extensions, compressions ]
65F10			[ Iterative methods for linear systems ]
65F50			[ Sparse matrices ]
65R20			[ Integral equations ]

Abstract:

This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators which yields quasi-sparse system matrices. These matrices can be compressed such that the complexity for solving a boundary integral equation scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. Based on the wavelet Galerkin scheme we present also an adaptive algorithm. By numerical experiments we provide results which demonstrate the performance of our algorithm.

Keywords:

wavelets, multilevel preconditioning, matrix compression, adaptivity

Language:

English

Publication time:

3 / 2003