Extension of a TSMFM fast integral equation solver for the characterization of planar-3D structures with vertical components

This contribution deals with the extension of a so-called Thin stratified medium fast multipole (TSMFM) approach to allow the characterization of large structures with vertical components like probe feeds and vertical interconnects (vias) and finite dielectric regions embedded in a multilayered environment. First formulations of this type of fast integral equation solver were presented already in [2]. In a similar approach in [1],[3], a cumbersome decomposition in radiation and receiving patterns is performed, in contrast to this we use a generalized Green's function tensor containing all integrations with regard to the vertical directions leading to a more stringent and effective implementation. Together with special Laguerre type integration strategies on the branch cuts, the computational efficiency can be optimized furthermore.