A Highly Scalable Quantized Tensor-Train FDTD Framework for the Simulation of Three-Dimensional Electromagnetic Scattering Problems
Abstract
In this letter, a novel 3-D Finite-Difference Time-Domain (FDTD) framework is proposed that circumvents the costly volumetric scaling of conventional FDTD methods. By representing the electromagnetic fields as low-rank Quantized Tensor Trains (QTT), the memory requirements scale logarithmically with system size. Moreover, the various numerical operations that constitute the FDTD scheme can be efficiently implemented in this format, with their computational cost also exhibiting a logarithmic complexity. The simulation of systems in open space is enabled by the inclusion of a uniaxial PML. A validation example demonstrates that the method achieves excellent accuracy compared to the traditional full-grid (FG) FDTD method, while significantly reducing the required computational resources. Memory savings of several orders of magnitude are obtained, highlighting the potential of the proposed framework for the simulation of large multiscale electromagnetic systems.
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BibTeX
@misc{vanhaecke2026highly,
title = {{A Highly Scalable Quantized Tensor-Train FDTD Framework for the Simulation of Three-Dimensional Electromagnetic Scattering Problems}},
author = {Daan Vanhaecke and Emile Vanderstraeten and Dries Vande Ginste},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18755},
eprint = {2609.18755},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18755},
}
RIS
TY - UNPB
TI - A Highly Scalable Quantized Tensor-Train FDTD Framework for the Simulation of Three-Dimensional Electromagnetic Scattering Problems
AU - Daan Vanhaecke
AU - Emile Vanderstraeten
AU - Dries Vande Ginste
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18755
UR - https://arxiv.org/abs/2609.18755
AB - In this letter, a novel 3-D Finite-Difference Time-Domain (FDTD) framework is proposed that circumvents the costly volumetric scaling of conventional FDTD methods. By representing the electromagnetic fields as low-rank Quantized Tensor Trains (QTT), the memory requirements scale logarithmically with system size. Moreover, the various numerical operations that constitute the FDTD scheme can be efficiently implemented in this format, with their computational cost also exhibiting a logarithmic complexity. The simulation of systems in open space is enabled by the inclusion of a uniaxial PML. A validation example demonstrates that the method achieves excellent accuracy compared to the traditional full-grid (FG) FDTD method, while significantly reducing the required computational resources. Memory savings of several orders of magnitude are obtained, highlighting the potential of the proposed framework for the simulation of large multiscale electromagnetic systems.
ER -