  An implicit causal space-time Galerkin scheme applied to the contrast current
density volume integral equation gives rise to a marching-on-in-time scheme
known as the MOT-JVIE, which is accelerated and stabilized via a fully embedded
FIR filter to compute the electromagnetic scattering from high permittivity
dielectric objects discretized with over a million voxels. A review of two
different acceleration approaches previously developed for two-dimensional
time-domain surface integral equations based on fast Fourier transforms (FFTs),
leads to an understanding why these schemes obtain the same order of
acceleration and the extension of this FFT-acceleration to the
three-dimensional MOT-JVIE. The positive definite stability analysis (PDSA) for
the MOT-JVIE shows that the number of voxels for a stable MOT-JVIE
discretization is restricted by the finite precision of the matrix elements.
The application of the PDSA provides the insight that stability can be enforced
through regularization, at the cost of accuracy. To minimize the impact in
accuracy, FIR-regularization is introduced, which is based on low group-delay
linear-phase high-pass FIR-filters. We demonstrate the capabilities of the
FFT-accelerated FIR-regularized MOT-JVIE for a number of numerical experiments
with high permittivity dielectric scatterers.
