A Unified Dispersive Media and PML FDTD Formulation Based on the Matrix Exponential Method

A unified dispersive media and perfect matching layer (PML) finite-difference time-domain (FDTD) formulation based on the matrix exponential (ME) method is proposed for the simulation of dispersive media characterized by first-order lossy Debye (LD) model. The method introduces the dispersive model into the FDTD algorithm and converts the update equation into a first-order differential equation by using the ME method. By adjusting the arrangement of the elements of the initial matrix, an updated formula format is skillfully created that is identical to the ME-PML algorithm. The time dependence in the FDTD updating formula is removed by the analytical method, leading to a significant reduction of numerical error. In addition, a novel unified scheme is present to reduce the complexity of the simulation of dispersive material by combining the field updating equations and the ME-PML algorithm into one consistent formulation. The Fourier method was used to evaluate and confirm the stability of the algorithm. The performance of the algorithm, its numerical accuracy, and efficiency, were also verified through simulations of human body models. The simplicity and precision of the algorithm make it a powerful tool with the potential for applications in the fields of biological sciences and radio frequency technology.