Xikui Ma

A 3-D precise integration time-domain method without the restraints of the courant-friedrich-levy stability condition for the numerical solution of Maxwell's equations

In this paper, a new three-dimensional time-domain method for solving vector Maxwells equations, called the precise-integration time-domain (PITD) algorithm, is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on the precise-integration technique. It is shown that this method is quite stable even when the CFL condition is not satisfied. Although the memory requirement of the PITD method is much larger than that of the finite-difference time-domain (FDTD) method, this new algorithm is very appealing since the time step used in the simulation is no longer restricted by stability. As a result, computation speed can be improved. Therefore, if the minimum cell size in the computational domain is required to be much smaller than the wavelength, this new algorithm is more efficient than the FDTD scheme. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method. It is found that the accuracy of the PITD is independent of the time-step size.

An Efficient 2-D Compact Precise-Integration Time-Domain Method for Longitudinally Invariant Waveguiding Structures

Based on both the compact technique and the precise-integration (PI) technique, a 2-D compact precise-integration time-domain method (CPITD) is developed in order to mitigate the rapidly growing numerical dispersion errors of a recently proposed compact finite-difference time-domain (FDTD) algorithm with increased time-step size when modeling electrically large and longitudinally invariant waveguiding structures. The stability condition and the dispersion equation of the new algorithm are both derived analytically. The provided enhancement over the FDTD, compact FDTD, and the conventional PITD methods is exhibited through theoretical examination of the dispersion performance, and subsequently, validated by means of numerical experimentation. It is found that with the PI technique, the maximum limit of the time step allowable by the new algorithms stability criterion is much larger than the Courant-Friedrich-Levy limit of the compact-FDTD method, more particularly, numerical dispersion errors can be made nearly independent of time-step size, i.e., an appreciable reduction of numerical dispersion error is achievable at any time-step size in the simulations. Numerical experimentations of typical waveguide structures verify and validate the very promising theoretical results. This CPITD algorithm will be very useful in electrically large and longitudinally invariant waveguiding structures since the decreased number of grid points in the 2-D domain greatly reduces the memory requirements and also the overall computational time, and the PI technique nearly removes the impact of time-step size on the numerical dispersion, and as a consequence, significantly reduces numerical dispersion error for any time-step size.

A split-step-scheme-based precise integration time domain method for solving wave equation

Purpose – This paper aims to present a modified precise integration time domain (PITD) method for the numerical solution of 2D scalar wave equation. Design/methodology/approach – The split step (SS) scheme is applied to factorize the conventional PITD calculation into two sub-steps procedures and then field components can be updated along one spatial direction only in each sub-step. The perfectly matched layer (PML) absorber is extended to this method for modeling open region problems by using the stretched coordinate approach. Findings – It is shown that this method requires less computation time and storage space in comparison with the conventional PITD method, yet maintains the numerical stability despite using large time steps. Research limitations/implications – The WE-PITD method requires the divergence free region, which may be a limit on its usage. Hence, there is a challenge of using this technique in the 3D problems. Originality/value – Based on the SS scheme, the PITD method is used to solve th...

Numerical Stability and Dispersion Analysis of the Precise-Integration Time-Domain Method in Lossy Media

In this paper, both the numerical stability condition and dispersion relation of the precise-integration time-domain (PITD) method in lossy media are presented. It is found that the time step size of the PITD method is limited by both the spatial step size of the PITD method and the ratio of permittivity to conductivity. In numerical dispersion investigations, it is shown that: the numerical loss error of the PITD method is always positive; the numerical phase error of the PITD method can be positive or negative; the numerical loss and phase errors can be made nearly independent of the time step size; and as the spatial step size decreases, the amplitudes of the numerical loss and phase errors decrease. In good conductors, the numerical phase velocity of the PITD method is closer to the physical value as compared with the finite-difference time-domain method. The numerical phase anisotropy of the PITD method can be positive or negative. The numerical anisotropies of the PITD method in the 3-D case are usually larger than those in the 2-D case. There is a conductivity giving zero numerical phase anisotropy. These theoretical observations are confirmed by numerical experiments.

Numerical Analysis of Electromagnetic Scattering From a Moving Target by the Lorentz Precise Integration Time-Domain Method

A novel numerical method, referred to as Lorentz precise integration time-domain (Lorentz-PITD) method, is proposed to deal with the scattering problem from a moving conducting slab. Both the overset grid generation technique and the Lorentz transformation are employed in this method. By using the Lorentz transformation and the linear interpolation technique, the incident plane wave in the rest frame is introduced to the moving frame; the scattered fields are transformed from the moving frame to the rest frame. Numerical experiments validate the Lorentz-PITD method and show that the Lorentz-PITD method is more computationally efficient compared with the Lorentz finite-difference time-domain method. An accompanied find is that there must be a tradeoff between the applicable frequency range and the computation cost in the proposed method.

A Low-Dispersion Realization of a Rectangular Grid With PITD Method Through Artificial Anisotropy

Through using a nonuniform rectangular grid in the time-domain algorithm, the computational efficiency can be improved obviously, but the numerical anisotropic dispersion error is seriously deteriorative. In this letter, a rectangular grid with the precise-integration time-domain method through artificial anisotropy is proposed to reduce the numerical dispersion error of a rectangular grid. Both the stability condition and the numerical dispersion equation are obtained analytically, and the numerical anisotropic dispersion of the proposed method is examined in detail. It is found that the numerical dispersion error can be reduced obviously and can also be made nearly independent of the time-step size. The numerical experiments validate and verify that the proposed method is of higher accuracy and efficiency.

A hybrid Krylov-subspace-exponential and finite-difference time integration approach for multiscale electromagnetic simulations

Purpose This paper aims to present a novel hybrid time integration approach for efficient numerical simulations of multiscale problems involving interactions of electromagnetic fields with fine structures. Design/methodology/approach The entire computational domain is discretized with a coarse grid and a locally refined subgrid containing the tiny objects. On the coarse grid, the time integration of Maxwell’s equations is realized by the conventional finite-difference technique, while on the subgrid, the unconditionally stable Krylov-subspace-exponential method is adopted to breakthrough the Courant–Friedrichs–Lewy stability condition. Findings It is shown that in contrast with the conventional finite-difference time-domain method, the proposed approach significantly reduces the memory costs and computation time while providing comparative results. Originality/value An efficient hybrid time integration approach for numerical simulations of multiscale electromagnetic problems is presented.

Numerical analysis of electromagnetic field in devices with the high-speed unit

Purpose The purposes of this paper are to numerically analyse the distribution of the electromagnetic field in the electromagnetic device wherein a high-speed unit exists and to develop a strong tool to analyse the evolution of an electromagnetic field tangled with moving parts. Design/methodology/approach The precise integration time domain (PITD) method and parameter weighted averaging approximation scheme. Findings It is shown that that the electromagnetic field in the device is significantly affected by the velocity of the moving unit and the parameters of the base material. The computation resources of the proposed method are saved and the efficiency is enhanced. Originality/value The parameter approximation (PA)-PITD method can be an effective and efficient time domain method to analyse the evolution of the electromagnetic field in electromagnetic devices with moving parts and similar problems.

A High-Order 2-D CPITD Method for Electrically Large Waveguide Analysis

Based on the fourth-order finite difference (FD) scheme, a modified compact two dimensional precise integration time domain (CPITD) method, called CPITD(4), is proposed to mitigate the numerical dispersion errors of the CPITD algorithm when modeling electrically large and longitudinally invariant wave-guiding structures. Both the stability condition and the dispersion equation of the CPITD(4) method are derived analytically. It is found that the dispersion error of the CPITD(4) method is much smaller than that of the CPITD method. In particular, it should be pointed out that the CPITD(4) method can improve the performance of the CPITD method when βz/β leaves away from 1. Numerical experiments of typical waveguide structures validate and verify that the CPITD(4) method can decrease the calculated error without increasing the memory requirement and the execution time for all the cases.

Efficient FDTD-PML Simulation of Gain Medium Based on Exponential Time Differencing Algorithm

An exponential time differencing (ETD) algorithm is introduced to incorporate the homogeneously broadened Lorentzian oscillator of gain medium in a four-level atomic system into the finite difference time domain (FDTD). Compared with the well known auxiliary differential equation (ADE) method, the proposed algorithm shows the same accuracy but can save one-third of the additional memory space for treating the Lorentzian oscillators, and has simpler formulations. The ETD implementation of the stretched coordinates perfectly matched layer (SC-PML) with the complex frequency shifted (CFS) stretching variable is applied to truncate computational domain with gain media. Simulations involving both TE and TM waves indicate that compared with the modified conventional PMLs and the convolution PML (CPML), the proposed absorbing boundary formulations can lead to a significant improvement of the absorbing performance with a similar memory requirement. Compared with the application of the material dependent PMLs to the gain media in previous studies, the proposed absorbing boundary condition has simpler formulas and can be applied to complex computational domains much more straightforwardly.