Large-Time-Step Operation in a Volume Integral Equation for Dielectric Scattering

Abstract

In transient electromagnetic analysis, explicit time-domain solvers are restricted by the Courant-Friedrichs-Lewy (CFL) condition, making finely discretized dielectric scattering problems computationally expensive. This work investigates large-time-step operation in a marching-on-in-time time-domain current-density volume integral equation (MOT-JVIE) solver for dielectric scattering. For the considered band-limited excitations, accurate transient analysis is demonstrated for time steps up to 16 times larger than the reference CFL-limited time step associated with the voxel discretization. The study reveals a fundamental computational shift in the large-time-step regime. As the time-step size increases, the present-time causal interaction region expands, increasing the number of nonzero entries in the present-time interaction matrix and causing the dominant computational cost to transition from history-term evaluations to repeated matrix--vector products involving this matrix. Consequently, the present-time interaction matrix emerges as the principal scalability bottleneck in the large-time-step regime. To address this bottleneck, a matrix-free FFT-based matrix--vector-product strategy that exploits the multilevel Toeplitz structure of the Green-function-related volume-integral operator is employed for the present-time interaction matrix. The proposed framework is evaluated through an inhomogeneous dielectric cube and an 8 X 8 array of inhomogeneous dielectric nanopillars representative of multiscale metasurface structures, demonstrating more than an order-of-magnitude reduction in computational cost. In single-threaded execution, the method is demonstrated for 15.6 million unknowns, providing a large-scale MOT-JVIE demonstration beyond 15 million unknowns on one CPU thread.