一種新型的高階時域有限差分方法
doi: 10.11999/JEIT190050
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安徽大學電子信息工程學院 合肥 230039
A New High Order Finite Difference Time Domain Method
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College of Electronic Information Engineering, Anhui University, Hefei 230039, China
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摘要:
相比于傳統(tǒng)高階時域有限差分算法(FDTD)而言,該文提出了一種改進的高階FDTD的優(yōu)化方法,該算法基于安培環(huán)路定律,通過計算機技術尋找到一組最優(yōu)的系數(shù)使得FDTD方法的全局色散誤差達到最小,通過不同分辨率下的點源輻射模擬證明了該方法在較低分辨率的情況下仍然具有極低的相位誤差,對于解決電大尺寸結構建模中的數(shù)值色散等問題提供了有效的解決方案。
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關鍵詞:
- 時域有限差分方法 /
- 相位誤差 /
- 優(yōu)化算法 /
- 安培環(huán)路定律
Abstract:Compared with the traditional high-order Finite Difference Time Domain(FDTD) Method, an improved high-order FDTD optimization method is proposed in this paper. This algorithm is based on Ampere’s law of circuits and finds a set of optimal coefficients through computer technology to minimize the global dispersion error of the FDTD method.The simulation of point source radiation with different resolutions shows that this method still has very low phase error in the case of lower resolution. It provides an effective solution to the problem of numerical dispersion in the modeling of large size structures.
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Key words:
- Finite Difference Time Domain(FDTD) /
- Phase error /
- Optimization algorithm /
- Ampere’s law
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表 1 部分分辨率的色散誤差
R K1 K2 ${\varPhi _{\gamma_i} }$ 5 –0.14493668 0.102073777 5.3797×10–10 10 –0.11619507 0.073446898 9.1959×10–14 15 –0.11180257 0.069281772 8.4433×10–16 20 –0.11032252 0.067892310 2.2994×10–17 25 –0.10964732 0.067260967 4.3034×10–18 30 –0.10928263 0.066920442 1.5703×10–19 35 –0.10906389 0.066716504 4.4814×10–20 下載: 導出CSV
表 2 4種情況下的運行時間和占用內(nèi)存對比
FDTD
方法運行
時間(s)占用
內(nèi)存(MB)空間
步長(m)時間
步長(s)粗網(wǎng)格 S22 0.0356 0.1 0.100 0.16×10–9 S24 0.0323 0.2 0.100 0.16×10–9 M24 0.0329 0.7 0.100 0.16×10–9 細網(wǎng)格 S22 77.3070 3.0 0.004 0.66×10–10 下載: 導出CSV
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