In this paper, the finite integration technique for the approximation of three-dimensional electromagnetic boundary value problems in the frequency domain is formulated for primal grids composed of either oblique parallelepipeds or oblique triangular prisms or tetrahedra, adopting as dual grid the barycentric subdivision of the primal one. Novel constitutive relations are in particular derived assuring solution matrices of symmetric and positive definite type

The finite difference-time domain algorithm is extended by means of finite integration technique to the case of tetrahedral primal grids. The resulting algorithm, unlike all previous attempts proposed in literature, is both explicit, consistent, and conditionally stable. It can be applied to both isotropic and anisotropic linear media. Numerical experiments demonstrate that the proposed algorithm leads to accurate approximations of the electromagnetic field

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