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Rapid solution of boundary integral equations by wavelet Galerkin schemes

In: Multiscale, Nonlinear and Adaptive Approximation

Author

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  • Helmut Harbrecht

    (Bonn University, Institute for Numerical Simulation)

  • Reinhold Schneider

    (Technical University of Berlin, Institute of Mathematics)

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.

Suggested Citation

  • Helmut Harbrecht & Reinhold Schneider, 2009. "Rapid solution of boundary integral equations by wavelet Galerkin schemes," Springer Books, in: Ronald DeVore & Angela Kunoth (ed.), Multiscale, Nonlinear and Adaptive Approximation, pages 249-294, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-03413-8_8
    DOI: 10.1007/978-3-642-03413-8_8
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