Time-dependent scattering by a bounded obstacle in three dimensions

Journal article, 1982

In the present paper we introduce a new method of treating the scattering of transient fields by a bounded obstacle in three dimensions. The method is a generalization to the time domain of the null field approach first given by Waterman. We define new sets of time-dependent basis functions, and use these to expand the free space Green's function and the incoming and scattered fields. The sacttering problem is then reduced to the problem of solving a system of ordinary differential equations. One way of solving these equations is by means of Fourier transformation, and this leads to an efficient way of obtaining the natural frequencies of the obstacle. Finally, we have computed the natural frequencies numerically for both a spheroid and a peanut-shaped obstacle for various ratios of the axes.