The Fourier boundary element method and its singularities

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 precomputed 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.     «

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 precomputed 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...     »