高阶准确的FDTD方案用于第二阶形式的色散麦克斯韦方程
High-Order Accurate FDTD Schemes for Dispersive Maxwell's Equations in Second-Order Form Using Recursive Convolutions
AI总结：
本文提出一种新的FDTD方案，用于求解具有线性色散效应的麦克斯韦方程，结合递归卷积方法实现高阶空间和时间精度，展示了二阶和四阶方案的稳定性分析。
摘要：
我们提出了一种新的有限差分时域（FDTD）方案，用于求解存在线性色散效应的麦克斯韦方程。该方法使用高阶空间和时间近似，将色散麦克斯韦方程写成第二阶向量波方程，并包含时间历史卷积项。修改方程方法与递归卷积（RC）方法结合，开发出高阶近似，可任意阶数准确。推导出高阶中心近似，以恢复不连续材料界面处的精度。展示了二阶和四阶方案，并在二维空间中实现Drude线性色散模型的情况。分析了这些方案的稳定性。最后，我们的方法如果与适当的广义拉普拉斯算子结合，也适用于曲线坐标系。
英文摘要：
We propose a novel finite-difference time-domain (FDTD) scheme for the solution of the Maxwell's equations in which linear dispersive effects are present. The method uses high-order accurate approximations in space and time for the dispersive Maxwell's equations written as a second-order vector wave equation with a time-history convolution term. The modified equation approach is combined with the recursive convolution (RC) method to develop high-order approximations accurate to any desired order in space and time. High-order-accurate centered approximations of the physical Maxwell interface conditions are derived for the dispersive setting in order to fully restore accuracy at discontinuous material interfaces. Second- and fourth-order accurate versions of the scheme are presented and implemented in two spatial dimensions for the case of the Drude linear dispersion model. The stability of these schemes is analyzed. Finally, our approach is also amenable to curvilinear numerical grids if used with appropriate generalized Laplace operator.
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