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.