### 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.