A hybrid UTD-eigenfunction method for scattering by a vertex

Present solution for the electromagnetic scattering by a vertex are either approximate or difficult to use for computations. For example, GTD solutions for vertex scattering are not yet fully developed and yield approximate results of unknown accuracy. The exact eigenfunction solution is both difficult to use and computationally inefficient due to the large number of eigenfunctions that must be retained. In this work, we obtain the scattering by a vertex (e.g., a quarter plane) by employing the exact eigenfunction solution only in a very small region close to the tip of the vertex (i.e., within 0.2 lambda). Thus, only a small number of eigenfunctions (e.g., two or three) are required to obtain the current in the top region. Outside of this region, the UTD is employed to obtain the current. The changeover point is determined by finding the point where the eigenfunction current has decayed to that predicted by UTD wedge diffraction theory. Results will be shown for both the current on the quarter plane and also for the scattered field. In addition, the field scattered by a rectangular plate using this method will be compared with that predicted by the UTD with vertex diffraction, and the results will be seen to be in very close agreement.