The exponential time differencing (ETD) formulation for the stretched coordinate perfectly matched layer (PML) is proposed through the Taylor expansion. This general D and B formulation can be used to truncate arbitrary media in the FDTD simulations. The numerical experiments validate the effectiveness of the ETD schemes. The computational efficiency of the ETD algorithm is identical to that of simple auxiliary differential equation method. The ETD is superior to any other implementation of the stretched coordinate and uniaxial PMLs. The optimum value of the effective relative permittivity for the inhomogeneous media can reduce the peak relative reflection error of the PML by about 15 dB relative to the average value. The performance of the PML is improved remarkably.

中文翻译：

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拉伸坐标完美匹配层的指数时差实现

通过泰勒展开提出了用于拉伸坐标完美匹配层 (PML) 的指数时间差分 (ETD) 公式。这种通用的D和B公式可用于在 FDTD 模拟中截断任意介质。数值实验验证了 ETD 方案的有效性。ETD算法的计算效率与简单辅助微分方程法的计算效率相同。ETD 优于拉伸坐标和单轴 PML 的任何其他实现。非均匀介质的有效相对介电常数的最佳值可以将 PML 的峰值相对反射误差降低约 15 dB 相对于平均值。PML 的性能显着提高。