Semi-analytical solution structures for solving electrodynamics boundary-value problems by the R-function method

In this report, a novel semi-analytical method is proposed. It is based on the fact that many types of domains (L-shaped, H-shaped, sectorial, etc.) may be considered as theoretical-set intersections of some canonical domains with other simple domains. So, it is possible to find the solution to the original Dirichlet boundary-value problem in the form of a generalized Fourier series with respect to eigenfunctions of one of the canonical domains. Since these eigenfunctions do not satisfy the Dirichlet conditions on some parts of the given domain boundary, the series must be multiplied by the function vanishing on these parts. The expression for this function is simpler than that for the function of the whole domain. Thus, the procedure of evaluation of coupling integrals is simplified essentially in comparison with that in the conventional R-function scheme.