Method of Generalized Debye Sources for the Analysis of Electromagnetic Scattering by Perfectly Conducting Bodies With Piecewise Smooth Boundaries

The method of generalized Debye sources, which is free from spurious resonances and the low-frequency breakdown, is extended to the case of electromagnetic scattering by perfectly conducting bodies with piecewise smooth boundaries. The method, originally proposed by Epstein and Greengard (2010), is based on the representation of the electromagnetic field via two fictitious surface charge densities referred to as generalized Debye sources. This representation enables one to reduce the problem of electromagnetic scattering to two scalar integral equations. In order to extend the method to the case of scatterers with piecewise smooth surfaces, additional conditions, expressing continuity of the fictitious currents on the edges of the scatterer´s surface, are introduced and an alternative technique for deriving one of the integral equations is applied. The algorithm implementation is demonstrated on the problem of electromagnetic scattering by a perfectly conducting cube. The numerical scheme in this case proved to be equally stable both in the low- and resonant-frequency regions. The method can be especially recommended for the computation of low-frequency fields.