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The finite integration technique (FIT) is combined with the uniform geometrical theory of diffraction (UTD) for the solution of radiation and scattering problems in complex environments. The presented hybrid formulation is capable of handling large objects allowing in the same time a precise modeling of important geometrical details and material inhomogeneities. The part of the structure which contains the details of the geometrical model and the material inhomogeneities is discretized and solved using the FIT discretization scheme, whereas the influence of the large scatterers to the total solution is resolved by means of UTD. In contrast with other finite-difference-based hybridizations, in the presented formulation the case of the strong coupling between the two subproblems without simplifications is considered. This is accomplished by introducing an appropriate boundary operator derived by the equivalence principle. The resulting equation system possesses a complex, nearly dense system matrix, which is difficult to handle even using iterative solvers. To overcome this difficulty the system of equations is solved using a two-step procedure, i.e., the FIT equation and the boundary condition are treated separately.