NASA NTRS1985
To represent the final results in terms of matrices, one expands all appropriate physical quantities in terms of partial wave basis states. This includes expansions for the incident and scattered fields and the surface quantities. The method then utilizes the Huygen-Poincare integral representation for both the exterior and interior solutions, leading to the required matrix equations. One thus deals with matrix equations, the complexity of which depends on the nature of the problem. It is shown that in general a transition matrix T can be obtained relating the incident field A with the scattered field f having the form T = PQ(-1), where f = TA. The structure of Q can be quite complicated and can itself be composed of other matrix inversions such as arise from layered objects. Recent improvements in this method appropriate for a variety of physical problems are focused on, and on their implementation. Results are outlined from scattering simulations for very elongated submerged objects and resonance scattering from elastic solids and shells. The final improvement concerns eigenfunction expansions of surface terms, arising from solution of the interior problem, obtained via a preconditioning technique. This effectively reduces the problem to that of obtaining eigenvalues of a Hermitian operator. This formalism is reviewed for scattering from targets that are rigid, sound-soft, acoustic, elastic solids, elastic shells, and elastic layered objects. Two sets of the more interesting results are presented. The first concerns scattering from elongated objects, and the second to thin elastic spheroids.