Rapid solution of boundary integral equations by wavelet Galerkin schemes

Helmut Harbrecht () and Reinhold Schneider ()
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Helmut Harbrecht: Bonn University, Institute for Numerical Simulation
Reinhold Schneider: Technical University of Berlin, Institute of Mathematics

A chapter in Multiscale, Nonlinear and Adaptive Approximation, 2009, pp 249-294 from Springer

Abstract: Abstract The present paper aims at reviewing the research on the wavelet-based rapid solution of boundary integral equations. When discretizing boundary integral equations by appropriate wavelet bases the system matrices are quasi-sparse. Discarding the non-relevant matrix entries is called wavelet matrix compression. The compressed system matrix can be assembled within linear complexity if an exponentially convergent hp-quadrature algorithm is used. Therefore, in combination with wavelet preconditioning, one arrives at an algorithm that solves a given boundary integral equation within discretization error accuracy, offered by the underlying Galerkin method, at a computational expense that stays proportional to the number of unknowns. By numerical results we illustrate and quantify the theoretical findings.

Keywords: Boundary Element Method; Boundary Integral Equation; Wavelet Base; Sparse Grid; Adaptive Wavelet (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-03413-8_8

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DOI: 10.1007/978-3-642-03413-8_8

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