Performances of absorbing boundary conditions on 2-D leapfrog alternating direction implicit FDTD
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摘要: 给出了两种适用于二维单步交替方向隐式时域有限差分(2-D Leapfrog ADI-FDTD)方法的吸收边界：Mur边界和卷积完全匹配层(CPML)边界。单步交替方向隐式时域有限差分(Leapfrog ADI-FDTD)方法是一种无条件稳定的全隐式差分算法，由于二维空间Leapfrog ADI-FDTD的迭代同时存在显式和隐式方程，故而不同电磁分量的边界条件也存在差异。从原理出发，推导了适用于2-D Leapfrog ADI-FDTD方法的CPML边界条件，并与一阶Mur边界进行比较，利用自由空间的反射误差来表征两种边界的吸收性能，简要总结了两种吸收边界的优缺点。
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关键词:
- Leapfrog ADI-FDTD /
- 无条件稳定 /
- Mur吸收边界 /
- CPML吸收边界 /
- 吸收性能
Abstract: This paper presents two kinds of absorbing boundaries for the two-dimensional (2-D) Leapfrog Alternating Direction Implicit Finite-Difference Time-Domain (Leapfrog ADI-FDTD) method—Mur boundary and CPML absorbing boundary condition. Leapfrog ADI-FDTD had unconditional stability and all the iterative equations were implicit. However, the electric and magnetic field components for the 2-D leapfrog ADI-FDTD method were updated implicitly as well as explicitly, absorbing boundary condition for difference components might keep diversity. Updating equations of CPML are presented in the paper according to its derived theory and compared with first-order Mur absorbing boundary condition. What's more, the reflection error of free space was used to represent absorbing ability of absorbing boundary condition. -
图 3 不同吸收边界下观察点的电场波形
Figure 3. Electric field waveform of observing point under different boundary condition
图 4 Mur边界与CPML边界的吸收性能
Figure 4. Absorbing performance of Mur and CPML boundary condition
表 1 两种吸收边界的耗时和内存比较
Table 1. Time and memory cost of two kinds of boundary condition
boundary mesh time/s memory/Mb Mur 60×60 109.65 19.56 CPML 60×60 135.08 25.59 
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