【摘要】 高阶辛时域有限差分法(S-FDTD)的稳定度及计算精度都较传统的时域有限差分法(FDTD)更为优越,在长时间数值仿真中的优势更加明显。本文从电磁场方程的Hamilton函数出发,提出了一种基于辛Runge-Kutta-Nystr m(SRKN)算法的S-FDTD方法,对该方法的稳定性和数值色散性进行了系统的探讨。计算结果表明与传统的高阶S-FDTD方法——辛Partitioned-Runge-Kutta(SPRK)比较,该方法计算速度和计算精度都有较大的提高。更多还原

【Abstract】 High-order symplectic finite-difference time-difference(S-FDTD)method is superior both in accuracy and speed to the conventional finite-difference time-difference method(FDTD).In this paper we describe a set of high-order FDTD schemes constructed using the symplectic Runge-Kutta-Nystrm integration techniques for Hamilton system.This method disperses the Maxwell equations in the time domain based on symplectic transformation,which can preserve the exchange-ability of the Hamilton system for phase space and the total energy.The stability and numerical dispersion analysis are included.Numerical examples are used to illustrate the gain in accuracy of the proposed method versus the conventional high order S-FDTD schemes based on Symplectic Partitioned-Runge-Kutta integration techniques.更多还原