A numerical analysis of electromagnetic scattering of perfect conducting cylinders by means of discrete singularity method improved by optimization process

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Abstract
As a method of solving the electromagnetic scattering by perfectly conducting cylinders, the discrete singularity method is discussed. For this method, a finite number of singular points is distributed within the scatterer and the wave function composed of a linear combination of solutions (each of which is derived from a Helmholtz equation with each single singularity among the many) is matched with the incident wave function on the boundary. the remaining important problem in this method is how to distribute these singularities in order to obtain the accurate solution with faster convergence and with fewer number of singular points for an arbitrary configuration of the scatterer. the purpose of this paper is to present a reasonable solution to this problem. the essential point of the method is that by making as unknown quantities, not only the unknown amplitude coefficients involved in the linear combination of the solutions, but also the coordinates of the singularities, the scattered wave is matched on the boundary in the sense of the least squares. This problem is linear in the amplitude coefficient but nonlinear in the singularity coordinate. Thus we solve this problem by using the algorithm by Marquardt et al. of a nonlinear optimization process. This paper considers the general description and indicates its effectiveness by showing a few examples of the scattering problem of rectangular cylinders.