IMPLICITNESS AND STABILITY OF TIME DOMAIN INTEGRAL EQUATION SCATTERING ANALYSES

Abstract

Time domain integral equation analysis of scattering problems has been inhibited by the instability generally observed. Usual treatments are explicit. We here describe an implicit approach, which allows timesteps to be selected to model the temporal variation of the field, rather than being constrained to small values by the need for the wave propagation during a timestep to be less than the smallest nodal spacing. For realistic bodies, this alone can result in computational cost savings by a significant factor. We present an investigation of the stability of the implicit approach, and show that it is much less prone to instability than the explicit. For realistic bodies, with rationally chosen timesteps, the implicit approach is for all practical purposes stable. This is so without recourse to the various temporal averaging schemes which have been proposed for stabilisation of the explicit form.