Louis Fishman
Dept. of Math. and Computer Sci., Colorado School of Mines, Golden, CO 80401
Recognizing that typical ocean propagation problems are essentially scattering problems in terms of a transition region and transversely inhomogeneous asymptotic half-spaces, wave-field splitting, invariant imbedding, and phase space methods have reformulated the problem in terms of an operator scattering matrix characteristic of the transition region. This approach solves the elliptic (fixed-frequency) scattering problem by well-posed marching (one-way) methods, and is centered on the reflection and transmission operator symbol equations. For several nontrivial, two-dimensional, refractive index profiles, these equations (and the wave-field equations) are solved exactly and analyzed. These results provide benchmark cases to test both the scattering operator and subsequent wave-field calculations, providing a severe test of the stiff nonlinear solvers employed in the numerical implementation of the method. The exactly solved models incorporate symmetric and asymmetric wells, trapped modes, and sharp-gradient features. Numerical results will be presented. [Work supported by NSF, AFOSR, ONR, ASEE, JEWC, and the S. N. Bose Centre for Basic Sciences.]