Numerical Solution for Transient Scattering from a Hard Surface of Arbitrary Shape

The problem of transient scattering from a hard surface S reduces to the solution of an integral equation for the potential at S. To facilitate numerical solution, S is divided into N zones, on each of which the potential is assumed constant, and time is also discretized. These approximations lead to a set of N algebraic equations relating the present values of the potential to the retarded values and to the incident field. When the zoning is done properly, each equation involves only one present value, and thus the potential can be calculated by a step‐by‐step numerical process. It is important to compute the coefficients in the N equations accurately; this is accomplished by a numerical technique that takes into account the curvature of the zones and the variation in time retardation across a zone. For scattering from a sphere, results agree very well with the exact solution. [Work supported by the U. S. Office of Naval Research.]