Bubnov-Galerkin solutions to wire-antenna problems

The current distribution on a linear antenna, formulated in terms of the Hallén integral equation, is approximated by interpolation polynomials whose coefficients are determined by the Bubnov-Galerkin projective method. The projection integrals contain nearly singular kernels, leading to computational difficulties. By defining suitable weighted Gaussian quadrature formulas, these difficulties can be avoided, permitting rapid evaluation of the integrals. The resulting computing times for this method are very fast, and the memory requirements are modest. Results are presented for a single dipole, and for Yagi-Uda arrays up to 32 elements. Good agreement is obtained with published experimental results in all cases.