Numerical treatment of classic scattering from bounded objects

Abstract

Classic scattering from objects of arbitrary shape must generally be treated by numerical methods. It has proven very difficult to describe scattering from general bounded objects without resorting to frequency-limiting approximations. The starting point of many numerical methods is the Helmholtz integral representation of a given wavefield. From that point several departures are possible for constructing computationally feasible approximate schemes. To date, attempts at direct solutions have been rare. One method (originated by P. Waterman) that attacks the exact numerical solution for a very broad class of problems begins with the Helmholtz integral representations for a point exterior and interior to the target in a partial wave expansion. After truncating the partial wave space, one arrives at a set of matrix equations useful in describing the field. This method is often referred to as the T-matrix method, null-field, or extended integral equation method. It leads to a unique solution of the exterior boundary integral equation by incorporating the interior solution (extinction theorem) as a constraint. In principle, there are no theoretical limitations on frequency, although numerical complications can arise and must be appropriately dealt with for the method to be computationally reliable. For submerged objects the formalism will be outlined for acoustical scattering from targets that are rigid; sound-soft and penetrable; elastic solids; elastic shells; and layered elastic objects. Finally, illustrations of several numerical examples for the above will be presented to emphasize specific response features peculiar to a variety of targets.