M. C. van Beurden | Searcharxiv

arXiv2026

Causality-Aware Interaction Selection for Retarded Green-Function Assembly

In time-domain integral-equation (TDIE) solvers, the assembly of the retarded Green-function interactions remains a major computational bottleneck. We present a causality-aware assembly strategy that exploits the finite space--time support of the retarded Green function to identify admissible interactions prior to numerical evaluation. By using causality as an exact interaction-selection criterion, causally inadmissible interactions are excluded a priori, reducing assembly complexity without modifying the underlying TDIE formulation or introducing approximations. Numerical validation confirms that the proposed pruning preserves the TDIE transient response. The remaining admissible interactions are organized into vectorized shared-memory workloads for efficient assembly. The results demonstrate a 41 % reduction in evaluated interactions, a 2.6 times single-worker algorithmic speedup, and a total assembly-time speedup of up to 109 times using 64 CPU workers.

physics.optics↗

arXiv2026

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

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.

physics.optics↗