The treatment of scattering from submerged objects in an unbounded Abstract. environment is of considerable interest to both the academic and technological communities. Several approaches have yielded results for different classes of problems and have proven manageable for the free environment case. The problem of scattering in a confined environment has proven more difficult to formulate in a form useful for calculation due to the coupling of effects from the scattered object with that of the boundaries. The purpose of this work is to propose two numerical schemes that will adequately describe scattering from realistic objects in a confined environment. Some of the realistic objects that are of interest are elongated objects such as spheroids and cylinders with rounded end-caps. Boundary conditions of interest range from those associated with rigid objects to those associated with elastic shells. We propose to examine the object in a waveguide problem in approximate numerical schemes rather than to attempt to solve the problem exactly. In each of the approaches under study, the starting point will be the solution of the problem in the vicinitv of the target. This will be obtained using a transition matrix that relates , vthe incident field to the scattered field. The transition matrix which is obtained from the Extended Boundan, Condition (EBC) method of Waterman does not account for boundaries other thah that of thd objdct. We then couple the solution with a waveguide solution to satisfy all boundary conditions. The methods that couple the solutions will be described. By appropriately coupling the two solutions we can satisfy all boundary conditions and preserve continuity of the solution throughout all space. The two most important methods that couple the solutions are: Source Term method and an applications of Huygens' principle.
The Source Term method treats the field scattered in the vicinity of the object as a secondary source which drives an inhomogeneous Helmholtz equation which in turn satisfies the exterior boundary condition. This method lends itself to a manageable perturbation treatment. The application of Huygens principle leads to a manageable direct solution of the problem. This method also satisfies all appropriate boundary conditions and yields a continuous solution throughout space. Details of these methods will be presented.