Calculation of the Impedance Matrix Inner Integral to Prescribed Precision

摘要

We present a new method for evaluating the inner integral of the impedance matrix element in the traditional Rao-Wilton-Glisson formulation of the method of moments for perfect conductors. In this method we replace the original integrand (modified by a constant phase factor) by its Taylor series and keep enough terms to guarantee a number of significant digits in the integration outcome. We develop criteria that relate the number of Taylor terms to the number of required significant digits. We integrate the leading Taylor terms analytically and the rest through iteration formulas. We show that the iteration formulas converge for all observation points within a sphere with a radius of half-a-wavelength and center the triangle's centroid. We compare results of our method with existing ones and find them in excellent agreement. We also outline a procedure for using cubatures outside the region of convergence.