  Self consistent solution to electromagnetic (EM)-circuit systems is of
significant interest for a number of applications. This has resulted in
exhaustive research on means to couple them. In time domain, this typically
involves a tight integration with field and non-linear circuit solvers. This is
in stark contrast to coupled analysis of linear/weakly non-linear circuits and
EM systems in frequency domain. Here, one typically extracts equivalent port
parameters that are then fed into the circuit solver. Such an approach has
several advantages; (a) the number of ports is typically smaller than the
number of degrees of freedom, resulting in cost savings; (b) is circuit
agnostic. A port representation is tantamount to an impulse response of the
linear EM system. In time domain, the deconvolution required to effect this is
unstable. Recently, a novel approach was developed for time domain integral
equations to overcome this bottleneck. We extend this approach to time domain
finite element method, and demonstrate its utility via a number of examples;
significantly, we demonstrate that the coupled and port parameter solutions are
identical to desired precision for non-linear circuit systems.
