Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

The Fourier boundary element method and its singularities

Fabian Duddeck
BMW Group, EK-212, Center of Research and Innovation, Knorrstrasse 147, Munich D-80636, Germany

  Full Text
One of the limitations of boundary element methods (BEM) lies in their need for a fundamental solution. In many engineering problems, this function is not known analytically but constructed numerically. The corresponding pre-computed values are stored in tables and later – during the computation – the required values are interpolated. To overcome this drawback and to accelerate the computation of the BEM, a Fourier transformed boundary element method was proposed. The focus of this paper is the treatment of singular and hypersingular integrals of this Fourier BEM. It can be shown easily that all strong and hypersingular values cancel. The computation of the singular integrals is hence straightforward in the Fourier space and can be used in traditional BEM approaches.

Keywords:  Boundary element method; Engineering problems; Singular and hypersingular integrals; Distribution theory

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