The effect of numerical integration on MoM VIE solution for some isolated dielectric resonators

The MoM solution for some dielectric resonators is obtained using volume integral equation (VIE) and zeroth-order edge basis functions. Variable degree of accuracy is implemented for integrals of the moment matrix. The most accurate case uses analytical formulas for all potential integrals including both self- and cross-terms. The non-singular part is found using Gaussian cubature up to 9^th degree of accuracy for tetrahedra and 10^th degree for faces. Convergence of the solution for the resonant frequency and Q-factor of the lowest (TE) mode is investigated. It is observed that the convergence for larger meshes does not improve with increasing the integration accuracy. Moreover, the center-point integral approximation consistently provides significantly better results for finer meshes. An explanation to this effect is suggested and discussed.