Comb Tensor Network Finite-Difference Time-Domain Algorithms for 2D and 3D Electromagnetic Simulations
This paper presents efficient 2D and 3D finite-difference time-domain (FDTD) algorithms augmented by the comb tensor network (CTN) representation of the field and auxiliary quantities. The proposed CTN-FDTD algorithm leverages superior compressibility of CTN compared with quantized tensor train (QTT), and rank-reduction strategies including local and global smoothing techniques to achieve logarithmic memory requirement and computation (per time step) cost. Numerical examples validate these complexities and demonstrate the applicability of CTN-FDTD using a variety of source excitation, frequency and permittivity profiles in both 2D and 3D. Remarkably, CTN-FDTD can simulate 35 trillion spatial grid points in 3D with low memory and computation costs on one computation node, whereas standard FDTD would require 281 TB memory to store each of its 31 3D arrays. Moreover, CTN-FDTD was applied to realistic 2D photonic crystal structure simulation with one million grid points and 3D scattering analysis with 8.6 billion grid points.