ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

4aUW6. A numerical solution of the parabolic elastic wave equation.

Raymond J. Nagem

Dept. of Aerospace and Mech. Eng., Boston Univ., 110 Cummington St., Boston, MA 02215

Ding Lee

Naval Undersea Warfare Ctr., New London, CT

Gongquin Li

Univ. of New Orleans

Based on the parabolic equation approximation, a set of equations has been developed for three-dimensional time-harmonic wave propagation in an elastic medium. The elastic equations for the scalar and vector potentials are written in a matrix form which is a direct counterpart to previous work on the scalar wave equation for a fluid medium. An ordinary differential equation (ODE) method in conjunction with a finite-difference scheme leads to a stable marching procedure. One feature of this approach is that every finite-difference discretization results in a tridiagonal system of equations; these equations can be solved efficiently by recursive formulas. This paper reports the computational results which are used to check (1) the stability of the marching scheme, and (2) the accuracy of the elastic model. Accuracy and validity are verified by comparing the numerical results of the finite-difference method with a far-field analytic solution in an unbounded medium.