标题： 求解时变麦克斯韦方程的数值方法 显示英文标题

标题： Numerical methods for solving the time-dependent Maxwell equations

摘要： 我们回顾了近期在数值算法方面的一些发展，这些算法用于求解具有空间变化的介电常数和磁导率系统的时变麦克斯韦方程。 我们展示了Suzuki积公式方法可以用来构造一族无条件稳定的算法，传统的Yee算法，以及两种不需要使用交错时间网格的新Yee算法变体。 我们还考虑了一种基于切比雪夫多项式展开的一阶算法，并比较了一阶算法、Yee型算法、交替方向隐式算法和无条件稳定算法的计算效率。 对于主要关注长时间行为的应用，我们发现一阶算法可能比现有的多时间步有限差分时域算法高效几个数量级。 显示英文摘要

摘要： We review some recent developments in numerical algorithms to solve the time-dependent Maxwell equations for systems with spatially varying permittivity and permeability. We show that the Suzuki product-formula approach can be used to construct a family of unconditionally stable algorithms, the conventional Yee algorithm, and two new variants of the Yee algorithm that do not require the use of the staggered-in-time grid. We also consider a one-step algorithm, based on the Chebyshev polynomial expansion, and compare the computational efficiency of the one-step, the Yee-type, the alternating-direction-implicit, and the unconditionally stable algorithms. For applications where the long-time behavior is of main interest, we find that the one-step algorithm may be orders of magnitude more efficient than present multiple time-step, finite-difference time-domain algorithms.