Application of the method of auxiliary sources for the spherical and ellipsoid resonators

In the previous work [1] there was shown the efficient application of the Method of auxiliary sources (MAS) for the problems of Eigen frequencies and electromagnetic resonator's Eigen Fields. The calculations for numerical results were conducted for 2D case, when the resonator is bounded by the cylindrical surface. There was shown the efficiency of the proposed method in comparison to the traditional method, based on the numerical solution of the linear algebraic equations homogenous system. In the given work there is considered the 3D case with the examples of the spherical and elliptical resonators. There is investigated the error of the solution and the boundary condition satisfaction. The short description of the corresponding theory is given below. After that there is considered some numerical results of volume resonators' excitation in order to determine their Eigen frequencies and Eigen fields.