Numerical Solution for Transient Scattering from a Hard Surface of Arbitrary Shape—Retarded Potential Technique

The problem of transient scattering from a hard surface S reduces to the solution of an integral equation for the potential at S. To allow numerical solution, S is divided into K zones, on each of which the potential is assumed constant, and time is also divided into discrete intervals. These approximations lead to a set of K 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, which can therefore be calculated explicitly from the retarded values. It is important to compute the coefficients in the K equations accurately. This is accomplished by a numerical technique which takes into account the curvature of the zones and the variation in time retardation across zone. For scattering from a sphere, results agree very well with those obtained by separation of variables.