Analytical evaluation of matrix elements of electromagnetic integral equations with RWG basis functions for arbitrarily oriented pairs of triangular surface elements

摘要

We present an approach to calculation of matrix elements for arbitrarily oriented planar surface elements, based on reduction of the surface integrals to line integrals over perimeters of the elements. The described method is a generalization of our previous developments applicable to parallel geometry elements; it utilizes a representation of the Helmholtz-equation Green function in terms of an auxiliary function acted upon by a differential operator involving tangential gradients in two different planes. Integration by parts allows then reduction of surface-to line integrals with nonsingular integrands. The latter integrals can be either evaluated as standard quadratures or expressed analytically, in every order of expansion in the wave number k, in closed form. The method can be applied to all operators arising in Maxwell equations and in similar problems in acoustics and elastodynamics, offering significant advantages in accuracy and the computational cost.