Accuracy improvement of the second-kind integral equations for generally shaped objects

In computational electromagnetics, second-kind integral equations are usually considered less accurate than their first-kind counterparts. The loss of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the previous studies, it was shown that by using the Buffa-Christiansen (BC) functions as testing functions, such a discretization error can be suppressed significantly, and the numerical accuracy of the second-kind IEs in the far-field calculation for spherical objects can be improved dramatically. In this paper, this technique is generalized for generally shaped objects in both perfect electric conductor and dielectric cases by using the BC functions as the testing functions, and by handling the near-singularities in the evaluation of the system matrix elements carefully. The extinction theorem is applied for accurate evaluation of the numerical errors in the calculation of scattering problems for generally shaped objects. Several examples are given to demonstrate the performance of this technique, and several important conclusive remarks are drawn.