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一種新型的高階時域有限差分方法

許杰,  徐珂,  黃志祥

許杰, 徐珂, 黃志祥. 一種新型的高階時域有限差分方法[J]. 電子與信息學報, 2020, 42(2): 425-429. doi: 10.11999/JEIT190050
引用本文: 許杰, 徐珂, 黃志祥. 一種新型的高階時域有限差分方法[J]. 電子與信息學報, 2020, 42(2): 425-429. doi: 10.11999/JEIT190050
Jie XU, Ke XU, Zhixiang HUANG. A New High Order Finite Difference Time Domain Method[J]. Journal of Electronics & Information Technology, 2020, 42(2): 425-429. doi: 10.11999/JEIT190050
Citation: Jie XU, Ke XU, Zhixiang HUANG. A New High Order Finite Difference Time Domain Method[J]. Journal of Electronics & Information Technology, 2020, 42(2): 425-429. doi: 10.11999/JEIT190050

一種新型的高階時域有限差分方法

doi: 10.11999/JEIT190050

  • 安徽大學電子信息工程學院 合肥 230039

基金項目: 國家自然科學基金(61722101, 61801002, 61701001, 61701003)，安徽大學物理科學與信息技術研究所開放式學科建設基金(2019AH001)
詳細信息
    作者簡介:

    許杰：男，1989年生，博士，研究方向為計算電磁學、高性能計算和時域數(shù)值算法

    徐珂：男，1991年生，博士，研究方向為計算電磁學、多物理仿真和時域數(shù)值算法

    黃志祥：男，1979年生，教授，博士生導師，研究方向為計算電磁學，電磁散射與逆散射

    通訊作者:

    黃志祥　zxhuang@ahu.edu.cn

  • 中圖分類號: O441.4

A New High Order Finite Difference Time Domain Method

  • College of Electronic Information Engineering, Anhui University, Hefei 230039, China

Funds: The Natural National Natural Science of China (61722101, 61801002,61701001, 61701003), The Open Fund for Discipline Construction, Institute of Physical Science and Information Technology, Anhui University (2019AH001)
  • 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。

    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.

    • HTML全文

  • 圖  1  高階FDTD方法示意圖

    圖  2  改進的高階FDTD算法示意圖

    圖  3  不同F(xiàn)DTD方法下的色散曲線

    圖  4  2維點源輻射模型

    圖  5  不同方法下點源輻射時域圖

    圖  6  矩形波導示意圖

    圖  7  不同方法下的S21參數(shù)曲線

    表  1  部分分辨率的色散誤差

    RK1K2${\varPhi _{\gamma_i} }$
    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S220.03560.10.1000.16×10–9
    S240.03230.20.1000.16×10–9
    M240.03290.70.1000.16×10–9
    細網(wǎng)格S2277.30703.00.0040.66×10–10
    下載: 導出CSV
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出版歷程
  • 收稿日期:  2019-01-17
  • 修回日期:  2019-08-28
  • 網(wǎng)絡出版日期:  2019-09-02
  • 刊出日期:  2020-02-19

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