A generalization of BEM by Fourier transform

To overcome the restriction of actual boundary element methods (BEMs) to cases where fundamental solutions are known we present here an alternative BEM-approach. It is based on new boundary integral equations (BIE) for the computation of the entries of the standard BEM matrices which are obtained by a spatial Fourier transform of the traditional BIE. In these equations, we only need 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. Non-linear problems can be solved by an iterative linear procedure. First applications for problems of isotropic and anisotropic Kirchhoff or Reissner plates are given. Due to the limited space, more complex examples will be presented in an additional paper.