Calculation of Impedance Matrix Inner Integral to Prescribed Precision for the Magnetic Field Integral Equation.

摘要

The Method of Moments (MoM) is a powerful computational electromagnetics method for analyzing antennas in situ. In a previous report, we presented a new method for evaluating the inner integral of the impedance matrix element in the traditional Rao-Wilton-Glisson formulation of MoM for the electric field integral equation. In this report, we extend our method to the magnetic field integral equation. We show how, in this case, the inner integral can be written in terms of two scalar integrals, a surface integral over the integration triangle (IT) and a line integral over the boundary of the IT. Just as with the original integral, neither of these integrals can be evaluated analytically. In our method, we bypass this obstacle by replacing the original integrand (modified by a constant phase factor) by its Taylor series and by keeping enough terms to guarantee a number of significant digits in the integration outcome. We have accomplished this for both the surface integral and the line integral. We present a systematic derivation of the formulas for the two integrals and we conduct an extensive testing of our results against quadratures and cubatures.