Fourier-BEM – What to do if there is no fundamental solution available?

The application of boundary element methods (BEM) to soil-structure interaction problems is still restricted to cases where fundamental solutions are known. Hence, a large number of engineering problems cannot be solved by the BEM. Therefore, an alternative approach is presented here which establishes new boundary integral equations (BIEs) for the computation of the entries of the BEM matrices by means of the spatial Fourier transform. For these alternative BIEs, we need only the transform of the fundamental solution and not the fundamental solution itself. The former is always available as long as the underlying differential operator is linear and has constant coefficients. The approach is possible for all variants of the BEM. For Galerkin approaches, the double integrations over the boundary panels are replaced by single integrations over the infinite domain.     «

The application of boundary element methods (BEM) to soil-structure interaction problems is still restricted to cases where fundamental solutions are known. Hence, a large number of engineering problems cannot be solved by the BEM. Therefore, an alternative approach is presented here which establishes new boundary integral equations (BIEs) for the computation of the entries of the BEM matrices by means of the spatial Fourier transform. For these alternative BIEs, we need only the transform of th...     »