路径积分方法在无源介质中的电磁脉冲传播
Electromagnetic pulse propagation in passive media by path integral methods
AI总结：
本文提出基于路径积分和伪谱方法的时域求解器，用于无源介质中麦克斯韦方程求解，无数值色散，指数收敛，高斯定律精确成立，且适用于时变介质。
摘要：
提出了一种在无源（色散和吸收）介质中求解麦克斯韦方程的新型时域求解器。该方法基于量子理论的路径积分形式，并涉及使用（i）哈密顿形式和（ii）求解微分方程的伪谱方法（特别是快速傅里叶变换）。与有限差分格式相比，基于路径积分的算法没有人为的数值色散（色散误差），在奈奎斯特极限下运行（波包中最短波长对应两个网格点），并且随着网格尺寸的增加表现出指数收敛，这反过来应导致更高的精度。高斯定律精确成立，且无额外计算成本。每个时间步需要O(N log2 N)次基本运算，其中N为网格尺寸。该方法还可用于模拟无源介质中电磁波的传播，当介质的性质随时间变化时，传统的稳态（散射矩阵）方法不适用。详细研究了算法的稳定性和精度。
英文摘要：
A novel time domain solver of Maxwell's equations in passive (dispersive and absorbing) media is proposed. The method is based on the path integral formalism of quantum theory and entails the use of ({\it i}) the Hamiltonian formalism and ({\it ii}) pseudospectral methods (the fast Fourier transform, in particular) of solving differential equations. In contrast to finite differencing schemes, the path integral based algorithm has no artificial numerical dispersion (dispersive errors), operates at the Nyquist limit (two grid points per shortest wavelength in the wavepacket) and exhibits an exponential convergence as the grid size increases, which, in turn, should lead to a higher accuracy. The Gauss law holds exactly with no extra computational cost. Each time step requires $O(N\log_2 N)$ elementary operations where $N$ is the grid size. It can also be applied to simulations of electromagnetic waves in passive media whose properties are time dependent when conventional stationary (scattering matrix) methods are inapplicable. The stability and accuracy of the algorithm are investigated in detail.
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