A Memory-Efficient PITD Method for Multiscale Electromagnetic Simulations

A memory-efficient variant of the precise-integration time-domain (PITD) method is proposed for multiscale electromagnetic simulations involving geometry details in only one or two dimensions. In the classic PITD method, the dense matrix exponential of the time-stepping operator arising from the finite difference discretization needs explicit evaluation and storage, leading to prohibitive memory costs. In the proposed method, the precise integration (PI) method is used to efficiently compute the sparse matrix exponential of a diagonal operator to obtain a transformation of the original ordinary differential equation (ODE) system, which has a relaxed stability criterion and can be integrated by any explicit time integration scheme. It is demonstrated by numerical experiments that the proposed method can exclude the stiffness due to directional geometry details and outperforms the classic finite-difference time-domain (FDTD) method in multiscale analysis.