A Highly Scalable Quantized Tensor-Train FDTD Framework for the Simulation of Three-Dimensional Electromagnetic Scattering Problems

This paper introduces a novel 3D Finite-Difference Time-Domain (FDTD) framework that employs Quantized Tensor Trains (QTT) for representing electromagnetic fields in a low-rank format. The approach overcomes the traditional cubic scaling limitation of FDTD methods by achieving logarithmic memory and computational complexity with respect to system size. The researchers demonstrate that numerical operations within the FDTD scheme can be efficiently implemented in the QTT format, making large-scale electromagnetic scattering simulations computationally tractable.