This work presents a hybrid finite element boundary integral algorithm to solve the problem of scattering from finite and infinite arrays of two-dimensional overfilled cavities engraved in a perfectly electric conducting flat screen. The solution region is divided into interior regions containing the cavities and their protruding portions, and the region exterior to the overfilled cavities. The finite element formulation is applied only inside the interior regions to derive a linear system of equations associated with field unknowns. Using two-boundary formulation, the surface integral equation employing the half-space Green’s function is applied on the boundary located at the interface of protruding portions of the cavities and the half-space as a boundary constraint to truncate the solution region. Placing the truncation boundary on the protruding portions of the cavities results in highly efficient solution in terms of computational resources, which makes the algorithm well suited for the optimization problems involving scattering from grating surfaces. The near fields are generated for finite and infinite arrays of overfilled cavities with different dimensions.
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