Helmut Harbrecht, Ulf Kähler, Reinhold Schneider:

Wavelet Matrix Compression for Boundary Integral Equations

Employing appropriate wavelet bases for the Galerkin discretization of boundary integral equations yields quasi-sparse system matrices. Discarding the nonrelevant matrix entries is called wavelet matrix compression. The compressed system matrix can be assembled within linear complexity if an appropriate $hp$-quadrature algorithm is used. Therefore, involving wavelet preconditioning, we arrive at an algorithm which solves a given boundary integral equation within discretization error accuracy, offered by the underlying Galerkin method, at a computational expense that is proven to stay proportional to the number of unknowns.

We intend to give an introduction on the wavelet-based fast solution of boundary integral equations. Besides the basic theory we present also recent developments concerning adaptivity and the extension to Tausch-White wavelets in order to treat also complicated geometries. By numerical experiments we provide results which corroborate the theory.

Bibliographical note: H. Harbrecht, U. Kähler, and R. Schneider: Wavelet Matrix Compression for Boundary Integral Equations, in Parallel Algorithms and Cluster Computing, Lecture Notes in Computational Science and Engineering, Vol. 52, edited by K.-H. Hoffmann and A. Meyer, Springer Berlin Heidelberg New York, pp. 129-149 (2006).

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[Thu Feb 19 18:56:37 2009]

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