A marching method for some elliptic models of wave propagation

Parabolic equation (PE) methods for wave propagation in the farfield are frequently obtained from elliptic equations valid in the farfield. Here, properties of the elliptic models are discussed directly. The equations are discretized and a marching method is obtained. Although the underlying initial value problems are not well posed, in certain parameter ranges, the marching method is stable when the step sizes are restricted in a suitable way. Under such restrictions, propagation loss curves are obtained that show good agreement with exact solutions of some test problems. Both fluid and elastic wave problems are considered. [Work supported in part by ONR.]