A time-domain surface integral equation approach based on the electric fiel
d formulation is utilized to calculate the transient scattering from both c
onducting and dielectric bodies consisting of arbitrarily shaped complex st
ructures. The solution method is based on the method of moments (MoM) and i
nvolves the modeling of an arbitrarily shaped structure in conjunction with
the triangular patch basis functions. An implicit method is described to s
olve the coupled integral equations derived utilizing the equivalence princ
iple directly in the time domain. The usual late-time instabilities associa
ted with the time-domain integral equations are avoided by using an implici
t scheme. Detailed mathematical steps are included along with representativ
e numerical results.