保角變換FDTD算法的數(shù)值穩(wěn)定性與數(shù)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變換FDTD算法，推導(dǎo)了保角變換FDTD算法的時(shí)間穩(wěn)定性和數(shù)值色散方程。此外，本文以圓波導(dǎo)為例計(jì)算了不同網(wǎng)格下TE模數(shù)值波長的相對(duì)誤差，分析了不同傳播常數(shù)和對(duì)極點(diǎn)不同半徑的半圓電壁近似下數(shù)值波長的相對(duì)誤差。通過適當(dāng)?shù)剡x擇網(wǎng)格數(shù)，可得到高精度。
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關(guān)鍵詞:
- 保角變換;FDTD算法;數(shù)值穩(wěn)定性;數(shù)值色散
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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