保角变换FDTD算法的数值稳定性与数值色散
NUMERICAL STABILITY AND NUMERICAL DISPERSION OF CONFORMAL MAPPING FDTD ALGORITHM
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摘要: 本文提出了新的保角变换FDTD算法，推导了保角变换FDTD算法的时间稳定性和数值色散方程。此外，本文以圆波导为例计算了不同网格下TE模数值波长的相对误差，分析了不同传播常数和对极点不同半径的半圆电壁近似下数值波长的相对误差。通过适当地选择网格数，可得到高精度。Abstract: This paper proposes a new algorithm based on conformal mapping and FDTD method,and derives the numerical stability and numerical dispersion equations of conformal mapping FDTD algorithm.As an example,the relative errors of numerical wavelengths for TE modes in a circular waveguide in different cell number are calculated.The errors for different propagation constants and for different radius semicircle electric wall approaches to singularity at origin are analyzed.By selecting cell number appropriately,high accuracy can be obtained.
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