A Plane Wave Scattering Dedicated Integral Equation

We present a variant of a boundary integral equation proposed by M. Herberthson in 2008–2010 for high-frequency plane wave scattering by perfectly conducting obstacles. This integral equation, as some of its predecessors, is entirely dedicated to a single direction of incidence. A significant reduction in the system size can then be obtained by looking for a pseudo-current, which is the actual surface current multiplied by the conjugate of the incident wave’s phase function. This advantage is mostly lost when multiincidence problems have to be solved because, in addition to the source terms, the discretized operator must be recomputed for every new incidence. In this article, we make an explicit representation of the new operator as the sum of a conventional electric field integral equation (EFIE) which is independent of the direction of incidence, and an additional operator, which is dependent on the direction of incidence. The latter can be computed very efficiently such that a net performance gain is obtained with respect to the EFIE even for multiincidence problems.