Tensor Train-Compressed FDTD Solvers for Electromagnetic Simulations

Finite-difference time-domain (FDTD)-based Maxwell equation solvers are widely used for solving scattering, radiation, resonance, circuit and wave propagation-related problems, due to their flexibility, simplicity and computational efficiency for modeling complex geometries and materials. Although FDTD is a linear-complexity algorithm, state-of-the-art solvers still need high-performance computing and parallel implementations to solve large-scale practical problems. This is particularly true when handling large complex geometries requiring either dense spatial discretization, subcell techniques, or conformal-cell techniques to address the stair-case discretization issues. In this work, we consider using tensor compression techniques to address these bottlenecks in the FDTD solvers.