ON THE CONVERGENCE AND NUMERICAL SENSITIVITY OF THE SEM POLE-SERIES IN EARLY-TIME SCATTERING RESPONSE

Abstract

The most general form of the Singularity Expansion Method (SEM) representation of the transient scattering response of a finite extent object allows considerable freedom of choice as to the time at which one begins to include the sum of residue contributions into the transient response--i.e., the “turn-on” time. The issue of the chosen form of the coupling coefficient used in computing these residue constituents relates intimately with the choice of turn-on time. The practical range of choices for turn-on time is considerably more restricted than the theoretical one. In this paper limitations on turn-on time are established in terms of the maximum geometric extent of the object and of the geometric extent of the object projected in the direction of propagation of the incident wave. These limitations are dictated in order to insure the convergence of the SEM residue series, and are, in general, different for the Class 1 and for the Class 2 coupling coefficient. It is further argued that the convergence of the series is more likely to be influenced by numerical error, if one attempts to apply the series too close to these bounds of turn-on time. This numerical sensitivity phenomenon is interpreted in terms of the sensitivity computation of the coupling coefficient integrals to pole error and supported with a numerical example. An optimum time origin location is determined to allow the earliest possible turn-on time for all possible incident angles and is found to be the center of the minimum sphere which circumscribes the object.