Two-Dimensional Radiation and Scattering at Short Wave Length

Abstract

The problem of radiation and scattering by objects in the case when the wave length is much smaller than the characteristic dimension of the radiator or scatterer is investigated. The boundary element method is used with the goal of obtaining accurate results in an efficient computational scheme for wave lengths less than 5 percent of the object characteristic dimension. With a systematic application of conventional boundary element techniques it is found that the modelling of such problems leads to excessive computation time due to the large number of elements, demands on Gaussian Quadrature, evaluation of the fundamental solution, and the resulting large nonsymmetric matrix equation. The approach is to use cubic elements, approximate polynomial and asymptotic evaluations of the fundamental solution, and to tailor the order of the Gaussian Quadrature according to the local demands dictated by the distance between sending and receiving points. In addition, out of core equation solvers are investigated. It is found that results can be obtained which are as accurate as those obtained using conventional Boundary Element techniques, but at greatly reduced cost. The potential application is to problems involving propagation of relatively low frequency sound over large terrain features.