圆柱坐标系下的网格波阻抗及其应用

从圆柱坐标系下麦克斯韦方程的时域有限差分式和特征解出发 ,引入了二维和三维圆柱坐标系下网格波阻抗 (MWI) .结合完全匹配吸收层 (PML)概念 ,推导出了二维圆柱坐标系下的MWI PWL吸收边界条件算法 .通过数值实验 ,研究了圆柱坐标系下网格波阻抗的正确性和它在圆柱坐标系下时域有限差分法 (FDTD)中的应用 .计算结果证明 ,当采用非均匀圆柱坐标系下FDTD法计算时 ,圆柱坐标系下网格波阻抗可以较准确地计算由于网格尺寸不同造成的数值反射误差 .同时 ,网格波阻抗也为确定网格尺寸容许可变的范围提供了理论标准 .二维圆柱坐标系下的MWI PML是一种简单、低反射的吸收边界条件 ,与Teixeira的完全匹配吸收层相比 ,其引起的数值反射误差增加不大但更易于实现 .

MWI in Cylindrical Coordinates and Its Application

Based on FDTD difference expressions and eigenfunctions of Maxwell functions in cylindrical coordinates, mesh wave impedances (MWIs) in 2D and 3D cylindrical coordinates were introduced. Combined with the concept of perfectly matched layer (PML), MWI PML absorbing boundary condition (ABC) algorithm was deduced in 2D cylindrical coordinates. Numerical experiments were done to investigate the validity of MWI and its application in cylindrical coordinates FDTD algorithm. The results showed that MWI in cylindrical coordinates can be used to accurately calculate the numerical reflection error caused by different mesh increments in non uniform FDTD. MWI can also provide theoretical criterion to define the permitted variable range of mesh dimension. MWI PML ABC is easy to be applied and reduces low numerical reflection, which only causes a little higher reflection error compared with Teixeira's PML.