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Description
This work presents a quantized tensor train (QTT)-accelerated finite-difference time-domain (FDTD) algorithm for solving Maxwell equations in 3D open domains.
Upon a QTT representation of both field variables and differential operators on uniform grids, the proposed algorithm can achieve up to logarithmic scaling in memory and per-step computational cost with respect to the number of spatial grid points. Our algorithm constitutes two major algorithmic contributions: (1) The integration of auxiliary differential equation perfectly matched layers (ADE–PML) directly in compressed form, enabling fully tensorized leapfrog time integration without decompression. (2) For complex excitations and media, QTT ranks can significantly grow due to both complex wave fields and numerical noise. To address this, we introduce spatial smoothing and filtering strategies that stabilize QTT ranks while preserving physical accuracy.
In summary, we demonstrate that classical explicit FDTD schemes can be fundamentally reinterpreted through QTT decompositions, providing new opportunities for scalable Maxwell solvers for large-scale and complex wave propagation simulations.