FFT-acceleration and stabilization of the 3D Marching-on-in-Time Contrast Current Density Volume Integral Equation for scattering from high contrast dielectrics

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 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 a 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.