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An interval finite element method for electromagnetic problems with spatially uncertain parameters

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Abstract

During the manufacturing process of dielectric materials used in electromagnetic engineering, the electromagnetic parameters are often spatially uncertain due to the processing technology, environmental temperature, personal operations, etc. Traditionally, the random field model can be used to measure the spatial uncertainties, but its construction requires a large number of samples. On the contrary, the interval field model only needs the upper and lower bounds of the spatially uncertain parameters, which requires much less samples and furthermore is easy to understand and use for engineers. Therefore, in this paper, the interval field model is introduced to describe the spatial uncertainties of dielectric materials, and then an interval finite element method (IFEM) is proposed to calculate the upper and lower bounds of electromagnetic responses. Firstly, the interval field of the dielectric material is represented by the interval K-L expansion and inserted into the scalar Helmholtz wave equations, and thus the interval equilibrium equations are constructed according to the node-based finite element method. Secondly, a perturbation interval finite element method is developed for calculating the upper and lower bounds of electromagnetic responses such as the electric strength and magnetic strength. Finally, the effectiveness of the proposed method is verified by three numerical examples.

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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 & Teng Fang

  2. Key Laboratory of Electronic Equipment Structure Design of Ministry of Education, School of Electro-Mechanical Engineering, **dian University, **’an, 710071, China

    CongSi Wang

  3. Nan**g Research Institute of Electronics Technology, Nan**g, 210039, China

    JianFeng Zhong

Authors
  1. ZhongHua Wang
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  2. Chao Jiang
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  3. BingYu Ni
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  4. CongSi Wang
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  5. JianFeng Zhong
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  6. Teng Fang
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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) and the Major Program of National Science Foundation of China (Grant No. 51490662).

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Wang, Z., Jiang, C., Ni, B. et al. An interval finite element method for electromagnetic problems with spatially uncertain parameters. Sci. China Technol. Sci. 63, 25–43 (2020). https://doi.org/10.1007/s11431-019-9671-7

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  • DOI: https://doi.org/10.1007/s11431-019-9671-7

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