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Uncertain eigenvalue analysis of the dielectric-filled waveguide by an interval vector finite element method

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Abstract

Eigenvalues of the dielectric-filled waveguide are of great importance to its transmission characteristic analysis and optimization design, which could be easily affected by spatially uncertain dielectric parameters. For the sake of quantifying their influence on eigenvalues of the dielectric-filled waveguide and overcoming the limitation of less samples, an interval vector finite element method (IVFEM) is proposed to acquire the lower and upper bounds of the eigenvalues with spatial uncertainty of the medium parameters Firstly, the uncertain dielectric material properties are described by the interval field model and the corresponding interval Karhunen-Loève (K-L) approximate method. Secondly, by inserting the interval uncertainties into the constitutive relationship of the standard generalized eigenvalue equations of the dielectric-filled waveguide, an interval standard generalized eigenvalue equation is then formulated. At last, the lower and upper bounds of the eigenvalues are calculated according to the first-order perturbation method, which can be used to estimate the transmission properties of the waveguide efficiently. Three kinds of the dielectric-filled waveguides are analyzed by the proposed IVFEM and verified by Monte Carlo simulation method.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China

    ZhongHua Wang, Chao Jiang, BingYu Ni, JinWu Li, Jing Zheng & ZhongYang Yao

Authors
  1. ZhongHua Wang
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  2. Chao Jiang
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  3. BingYu Ni
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  4. JinWu Li
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  5. Jing Zheng
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  6. ZhongYang Yao
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Corresponding author

Correspondence to Chao Jiang.

Additional information

This work was supported by the National Science Fund for Distinguished Young Scholars (Grant No. 51725502), the National Natural Science Foundation of China (Grant No. 11802089), and the National Defense Fundamental Research Foundation of China (Grant No. JCKY2020110C105).

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Wang, Z., Jiang, C., Ni, B. et al. Uncertain eigenvalue analysis of the dielectric-filled waveguide by an interval vector finite element method. Sci. China Technol. Sci. 65, 336–346 (2022). https://doi.org/10.1007/s11431-021-1940-y

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  • DOI: https://doi.org/10.1007/s11431-021-1940-y

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