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

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 measu...

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Bibliographic Details
Published in:Science China. Technological sciences 2020, Vol.63 (1), p.25-43
Main Authors: Wang, ZhongHua, Jiang, Chao, Ni, BingYu, Wang, CongSi, Zhong, JianFeng, Fang, Teng
Format: Article
Language:English
Subjects:
Dielectrics
Electric strength
Engineering
Equilibrium equations
Fields (mathematics)
Finite element analysis
Finite element method
Lower bounds
Mathematical models
Nonlinear programming
Parameter uncertainty
Perturbation
Process parameters
Wave equations
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Summary: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.
ISSN:1674-7321
1869-1900
DOI:10.1007/s11431-019-9671-7