Advanced Numerical Schemes for the Accurate Evaluation of 4-D Reaction Integrals in the Method of Moments

In this paper, we present a simple and efficient fully numerical technique for the evaluation of 4-D reaction integrals arising in the method of moments. In the proposed approach, the accuracy of the source integration, which uses a singularity cancellation scheme, is retained in the final 4-D reaction integral through the application of an appropriate variable transformation and numerical quadrature scheme to the test integral. Several numerical results compared to the usual Gauss-Legendre test quadrature demonstrate the accuracy of the method for both planar and curvilinear discretizations. Moreover, the proposed scheme is independent of test basis functions; hence, it can be used for higher order basis functions as well as curl-conforming or Buffa- Christiansen test basis functions.