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Recently, a powerful hybrid numerical method was introduced, combining the finite element boundary integral (FEBI) method and the multilevel fast multipole method (MLFMM) with the Uniform geometrical theory of diffraction (UTD), in which single and multiple reflections on flat metallic objects, combined with single diffractions on straight metallic edges, were considered. In this contribution, the hybrid FEBI-MLFMM-UTD method is extended to double diffraction high-frequency fields on pairs of straight metallic edges, formulated with the hard and soft scalar diffraction coefficients of the UTD. The diffraction points on each pair of edges are determined by a 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, acceleration of the near-field computations 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. The corresponding formulations, as well as numerical results are presented.