  This paper proposes a fast time-domain boundary element method (TDBEM) to
solve three-dimensional transient electromagnetic scattering problems regarding
perfectly electric conductors in the classical marching-on-in-time manner. The
algorithm of the fast TDBEM is a time-domain variant of the interpolation-based
fast multipole method (IFMM), which is similar to the time-domain IFMM for
acoustic scattering problems investigated in the author's previous studies. The
principle of the present IFMM is to interpolate the kernel functions of the
electric and magnetic field integral equations (EFIE and MFIE, respectively) so
that every kernel function is expressed in a form of separation of variables in
terms of both the spatial and temporal variables. Such an expression enables to
construct a fast method to evaluate the scalar and vector potentials in the
EFIE and MFIE with using so-called multipole-moments and local-coefficients
associated with a space-time hierarchy. As opposed to $O(N_s^2 N_t)$ of the
conventional TDBEM, the computational complexity of the fast TDBEM is estimated
as $O(N_s^{1+\delta}N_t)$, where $N_s$ and $N_t$ stand for the spatial and
temporal degrees of freedom, respectively, and $\delta$ is typically $1/2$ or
$1/3$. The numerical examples presented the advantages of the proposed fast
TDBEM over the conventional TDBEM when solving large-scale problems.
