Advances in hybrid finite element - Boundary integral - multilevel fast multipole - uniform geometrical theory of diffraction method

Numerical modeling of problems including composite metallic/dielectric objects with arbitrary shapes and electrically large conducting objects within a common environment is performed in an optimum way with the recently developed powerful hybrid numerical method, which combines the Finite Element Boundary Integral (FEBI) method and the Multilevel Fast Multipole Method (MLFMM) with the Uniform Geometrical Theory of Diffraction (UTD), giving full electromagnetic coupling between all involved objects. In this contribution, the hybrid FEBI-MLFMM-UTD method is extended to double diffracted fields on pairs of straight metallic edges, formulated with the hard and soft scalar diffraction coefficients of UTD. The diffraction points on each pair of edges are determined by an iterative three-dimensional parametric realization of the generalized Fermat's principle. The divergence factor of the double diffracted field is computed by multiplying the appropriate divergence factors of the single diffracted UTD fields on each edge for the particular case. Thereby, the ray caustic distance of the diffracted field at the second edge is determined by linear interpolation between the radii of curvature in the two principal planes of the incident astigmatic ray tube. Further, fast near-field computation in the postprocessing stage of the hybrid method is extended in each translation domain to ray optical contributions due to the presence of electrically large objects, according to the hybridization of MLFMM with UTD. Formulations and numerical results will be presented.