Solution of Radiation and Scattering Problems by Integral Equations

Abstract

Several recent methods for the calculation of the radiation field of an arbitrary vibrating surface, or the field scattered by a rigid obstacle are shown to reduce to solutions of integral equations, where the kernel function and the surface of integration are the same in all methods. The kernel function is usually replaced by a matrix of terms that are defined at only a finite number of stations, and thus the integral equation is approximated by a set of simultaneous algebraic equations. Hence, the comparative accuracy of the different methods depends mostly on the procedures used in selecting the stations and evaluating the matrix terms. A new method is described in which the surface stations are selected with arbitrary spacing, and the surface element about each point is approximated by a spherical cap whose curvature, inclination, and area match those of the local surface element. The method is illustrated by the problem of a vibrating piston on a sphere, and compared with solutions based on triangular and ringshaped surface elements.