Determination of the DC steady-state current density distribution using FDTD and analytical techniques

This paper examines the application of the FDTD method to the determination of the DC steady-state current density distribution of arbitrary geometries when the excitation is an impressed current. The term DC is used in this context to denote the response of a system to any waveform which tends asymptotically to a non-zero constant. Thus, more general waveforms than the unit step function can be considered. By concentrating on the steady state only (or, equivalently, the late time response) certain physical and mathematical difficulties can be circumvented. First, by definition of DC, there is no time variation so that the problem can be formulated in terms of an electrostatic potential, which is obviously more convenient than the magnetic vector potential needed in the time-dependent case. Additionally, assuming that the released heat is such that the temperature of the system (and hence the conductivity) remains almost constant, the thermal and electrical problems can be considered to be decoupled.