Analysis of various numerical techniques applied to thin-wire scatterers

Seven numerical methods for solving Pocklington's and Hallen's equations for thin-wire scatterers are investigated along with the relative convergence rates of the solutions obtained by these methods. The methods make use of different basis sets for representing the unknown wire current, and only the case of a scatterer subject to normally incident illumination is considered. It is shown that solution methods applied to Pocklington's equation must incorporate means of suppressing discontinuities in the current approximation and its derivative, and that the detrimental effects of these discontinuities must be eliminated by rendering the equation insensitive to them. Solutions by the difference equation method attain a high rate of convergence essentially identical to that of the point-matched Hallen equation.