A high-order on-surface radiation condition for computing scattering from concave objects and extended surfaces

Abstract

Approximate solutions to scattering problems can be obtained efficiently using on-surface radiation conditions (OSRCs). An OSRC may be viewed as an approximation of the exact nonlocal (integral) Dirichlet-to-Neumann operator, and therefore requires less effort to compute surface quantities and far-field patterns in comparison with other methods. In a previous study [Calvo et al., IEEE Trans. Antennas Propag. (in press)], a higher-order OSRC was developed for two-dimensional convex scatterers that was accurate for large scattering angles relative to the surface normal and moderate surface curvatures. A remarkable result was the exceptional accuracy obtained for end-on incidence with hard scatterers—a challenging case in which creeping waves arise and past OSRCs have had difficulty treating. In this talk, improvements to the OSRC are discussed by relaxing the convexity restriction to allow for compact objects with moderately deep concavity with favorable results. The OSRC is then applied to scattering by extended pressure-release surfaces featuring moderately deep corrugations. Results are favorable in comparison with other more costly numerical techniques. A particular advantage of the high-order OSRC occurs for grazing angles of incidence where the effects of shadowing come into play. Possible applications to ocean acoustics and microwave remote sensing of the sea surface will be addressed.