In this letter, the propagation of an electromagnetic (EM) wave in a time-variant medium is treated with a novel methodology stemming from the precise integration time domain (PITD) method. This methodology is a generalized version of the conventional PITD method (thus GPITD, for short). In the GPITD method, the electric displacement and the magnetic induction serve as the iteratively calculated components. In order to overcome the difficulty in implementing the precise integration (PI) routine caused by the time variation of the original coefficient matrix, an effective piecewise constant coefficient matrix is constructed. Both the numerical dispersion relation and the numerical stability condition of the GPITD method are described. Successful application of the GPITD method to solve the EM propagation problem associated with a layer whose permittivity suffers: 1) an abrupt change to a new value and 2) a sinusoidal modulation, confirms its effectiveness.

中文翻译：

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时变介质中电磁波的广义PITD数值处理

在这封信中，电磁 (EM) 波在时变介质中的传播使用源自精确积分时域 (PITD) 方法的新颖方法进行处理。这种方法是传统 PITD 方法（因此简称为 GPITD）的通用版本。在 GPITD 方法中，电位移和磁感应作为迭代计算的分量。为了克服原系数矩阵随时间变化导致的精密积分（PI）程序难以实现的问题，构造了一个有效的分段常系数矩阵。描述了GPITD方法的数值色散关系和数值稳定性条件。