Fast integral equation solver strategies with implicit matrix vector product evaluation for Planar-3D structures

This document describes the further development of a surface/volume fast integral equation solver for the effective characterization of Planar-3D structures in a multilayered environment consisting of an arbitrary number of planes carrying microstrip/stripline structures which can be connected with arbitrary vertical currents. For interactions with vertical volume currents, extended spectral domain Green's functions are computed on the Cartesian wavenumber plane and stored in a database. For the fast solver, these extended functions are used for the construction of diagonalized translation operators for the evaluation of implicit matrix-vector multiplications for the iterative solution of the linear system of equations generated by the method of moments (MoM). But for the accurate simulation of such structures, also a convergence problem in context with the near interactions of volume currents must be overcome. The different methods are used for the analysis of a directional coupler based on a mushroom-shaped metamaterial ground plane.