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Fast integral methods are used to improve the efficiency of hybrid finite element formulations for conformal antenna and array modeling. We consider here cavity-backed configurations recessed in planar and curved ground planes as well as infinite periodic structures with boundary integral (BI) terminations on the top and bottom bounding surfaces. Volume tessellation is based on triangular prismatic elements which are well suited for layered structures and still give the required modeling flexibility for irregular antenna and array elements. For planar BI terminations of finite and infinite arrays the adaptive integral method is used to achieve O(N log N) computational complexity in evaluating the matrix-vector products within the iterative solver. In the case of curved mesh truncations for finite arrays the fast multipole method is applied to obtain O(N1.5) complexity for the evaluation of the matrix-vector products. Advantages and disadvantages of these methods as they relate to different applications are discussed, and numerical results are provided.