ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

5aUW2. Range-stepping algorithm for the Helmholtz equation.

Dalcio K. Dacol

Naval Res. Lab., Washington, DC 20375-5350

The usual range-stepping algorithms used to obtain an approximate solution to the Helmholtz equation are based on the parabolic approximation and restricted to the forward propagating component of the solution. A complete solution of the Helmholtz equation in an inhomogeneous medium must also include backpropagating waves, that is, waves scattered towards the source by inhomogeneities. The inclusion of such effects in a numerically feasible full-wave approach to acoustic propagation is a problem of continual interest in ocean acoustics. This problem has been studied using the method of coupled amplitudes. Theoretical developments on the application of this technique to ocean acoustics will be discussed as well as numerical applications to the ASA range-dependent benchmark problems. Numerical application of this method involves a fourfold increase in the number of arithmetic operations as compared with that required for solving the same problem using a PE approach. However, one does get the backscattered field and one not does have to approximate square roots of differential operators as one must do in the PE approach. Since an elliptic equation is being solved one encounters numerical instabilities; how to deal with them will be discussed.