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

TL;DR

This paper introduces an FFT-accelerated, stabilized Marching-on-in-Time scheme for 3D electromagnetic scattering from high permittivity dielectrics, enabling efficient simulations of large voxel models with improved stability.

Contribution

It extends FFT-based acceleration and FIR-regularization techniques to 3D MOT-JVIE, enhancing stability and efficiency for high contrast dielectric scattering problems.

Findings

Achieved significant acceleration in 3D MOT-JVIE computations.

Demonstrated stable and accurate simulations with over a million voxels.

Validated the method with numerical experiments on high permittivity scatterers.

Abstract

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.