Stability of scattering formulations with multiple elemental current excitations

The use of the equivalent incident current as the exciting function has been proven economical and efficient in several applications regarding planar problems. In this formulation, the excitation is expressed in the same language used for the unknown induced current, and is expanded into the same basis functions used for the induced current distribution. The current amplitudes on the scatterer for any elemental pulse-type excitation are referred to as pulse responses. Following their evaluation, the solution for any incident field can be synthesized as a weighted summation of the pulse responses. When the individual pulse responses are computed with a finite error, the combination of the pulse responses gives rise to an accumulated error. A physical model which can explain the course taken by the total error shows that if root-mean-square error is small enough, then the accumulation takes place in an oscillatory manner. The physical model is presented, followed by a numerical study which supports the model.<>