Hybrid2: combining the three-dimensional hybrid finite element-boundary integral technique for planar multilayered media with the uniform geometrical theory of diffraction

The fully three-dimensional (3-D) hybrid finite element (FE)-boundary integral (BI) technique is extended by further hybridization with the uniform geometrical theory of diffraction (UTD) resulting in a so-called hybrid² FE-BI-UTD approach. The formulation is capable of modeling arbitrarily shaped strongly inhomogeneous objects together with electrically large obstacles of relatively simple shape within the common environment of a planar-multilayered medium. The arbitrarily shaped inhomogeneous objects are discretized by finite elements, whereas, the electrically-large obstacles are described by the UTD and both of these models are included into an integral equation derived from the equivalence principle for planar-multilayered media. Thus, full-electromagnetic coupling is realized between all parts of the formulation. The integral equation is implemented using mixed potentials with appropriate Green´s functions derived from Sommerfeld integral representations for planar-multilayered media. The UTD contributions are accounted for by corresponding modifications of the Green´s functions and the FE technique is coupled to the integral equation via introduction of equivalent surface current densities in the bounding surfaces of the discretized objects. After presenting the formulation of this novel fully 3-D hybrid² technique, the implemented computer code is validated against conventional hybrid FE-BI computations and a wireless base station antenna is analyzed in several situations of complex real world, microcell environments