A general boundary element method for homogeneous differential operators - Linear or nonlinear

For many engineering problems (e.g. anisotropic media) the fundamental solutions which are essential for boundary element methods (BEM) are not known analytically. Therefore, alternative boundary integral equations (BIE) are presented here which are obtained by a spatial Fourier transformation of the corresponding integral terms. In this transformed domain, the fundamental solution is always known and has a simple structure. Instead of transferring it back to the original domain (which is analytically often not possible) the already discretized unknowns are transferred into the transformed domain where all BIE are evaluated. The realization for isotropic and anisotropic plates (Kirchhoff) should visualize that this approach is possible for all homogeneous problems. First insights of the corresponding nonlinear BEM-formulations are given.