Tensor-Train FDTD: Implementation Aspects and Performance Analysis

Tensor-train (TT) decompositions have the potential to significantly improve the performance of finite-difference time-domain (FDTD) algorithms in terms of CPU time and memory storage. To this end, we extend TT-format FDTD implementations to cases incorporating perfectly matched layer (PML) boundaries. We assess the performance of TT-format FDTD implementations for different error tolerance levels. In particular, the tradeoff between accuracy and efficiency is analyzed. Additionally, a regularization approach is proposed to control rank growth in TT-format FDTD simulations with highly disparate field amplitude levels across the domain brought forth by PML absorption and diverse source excitations.