Impulse responses and the late time stability properties of time-domain integral equations

Impulse responses to the time-domain integral equations (TDIEs) using marching-on-in-time (MOT) scheme are discussed in this study. It can be seen clearly that the interior resonance currents are included in the impulse responses of the time-domain electric field integral equation (TDEFIE) and the time-domain magnetic field integral equation (TDMFIE), but not in those of the time-domain combined field integral equation (TDCFIE), while spurious DC solenoidal currents are only included in the TDEFIE. Analysis shows that the MOT-TDMFIE is basically exponentially convergent, and the MOT-TDCFIE usually converges to a small constant value, while the MOT-TDEFIE is basically unstable. The stability properties are justified by the eigenvalues of the corresponding systems. This study also shows that it is possible to solve time-domain integral equations (TDIEs) using their impulse responses truncated according to the maximum physical size of the scatterer.