Time-domain CFIE for the analysis of transient scattering from arbitrarily shaped 3D conducting objects

A time-domain combined field integral equation (CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three-dimensional (3D) conducting bodies. This formulation is based on a linear combination of the time-domain electric field integral equation (EFIE) with the magnetic field integral equation (MFIE). The time derivative of the magnetic vector potential in EFIE is approximated with the use of a central finite-difference approximation for the derivative, and the scalar potential is averaged over time. The time-domain CFIE approach produces results that are accurate and stable when solving for transient scattering responses from conducting objects. The incident spectrum of the field may contain frequency components, which may correspond to the internal resonance of the structure. For the numerical solution, both the explicit and implicit schemes are considered and two different kinds of Gaussian pulses are used, which may or may not contain frequencies corresponding to the internal resonance. Numerical results for the EFIE, MFIE, and CFIE are presented and compared with those obtained from the inverse discrete Fourier transform (IDFT) of the frequency-domain CFIE solution.