A higher-order on-surface radiation condition derived from an analytic representation of a Dirichlet-to-Neumann map

Abstract

An approximate solution to a scattering problem can be obtained efficiently using an on-surface radiation condition (OSRC) [G. A. Kriegsmann et al., IEEE Trans. Antennas. Propag. 35, 153–161 (1987)], which is an approximation of the Dirichlet-to-Neumann map. A higher-order OSRC is derived using an analytic representation of the Dirichlet-to-Neumann map for a circle, which involves a Hankel function with a tangential operator appearing in the index. This operator formalism is related to the well-known square root of an operator that arises in the parabolic equation method and is asymptotic to the square root in the high-frequency limit. The Hankel function is approximated with a rational function to obtain an OSRC for the circle. An OSRC for a more general convex object is obtained by fitting osculating circles to the surface and allowing the coefficients of the rational approximation to depend on curvature. Since the computation time increases only linearly with frequency, accurate solutions are obtained with substantial computational savings in comparison with other approaches. The OSRC can be constructed to any desired accuracy in scattering angle and surface curvature. [Work supported by ONR.]