A novel numerical method, referred to as the Riccati precise-integration time-domain (Riccati-PITD) method, is proposed to reduce the memory requirement of the conventional PITD method. In the Riccati-PITD method, the electromagnetic field components of the transverse electric/transverse magnetic (TE/TM) wave are arranged in a matrix for constructing the Riccati matrix differential equations (RDEs) about Maxwell’s curl equations. Then the precise integration technique is adopted for the numerical integration of the RDEs. Theoretical analyses about the memory requirements of the conventional and the Riccati-PITD methods are presented. It is found that the memory requirement can be more greatly reduced by solving the electromagnetic-field components in the form of the matrices in the Riccati-PITD method rather than in the form of the vectors in the conventional PITD method. Numerical examples are also given to confirm that the proposed method has significant advantages over the conventional PITD method with respect to the execution time and the memory requirement.

中文翻译：

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使用 Riccati 矩阵微分方程的精确积分时域方法的高效记忆公式

提出了一种新的数值方法，称为 Riccati 精确积分时域 (Riccati-PITD) 方法，以减少传统 PITD 方法的内存需求。在 Riccati-PITD 方法中，横向电/横磁 (TE/TM) 波的电磁场分量排列在矩阵中，用于构建关于麦克斯韦旋度方程的 Riccati 矩阵微分方程 (RDE)。然后采用精确积分技术对 RDE 进行数值积分。对传统方法和 Riccati-PITD 方法的内存要求进行了理论分析。发现在Riccati-PITD方法中以矩阵形式而不是在传统PITD方法中以向量形式求解电磁场分量可以更大幅度地减少内存需求。还给出了数值例子，以确认所提出的方法在执行时间和内存要求方面比传统的 PITD 方法具有显着优势。