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Boundary coefficient determination for an eddy current problem based on the potential field method

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Abstract

We study a recovery problem for an unknown boundary coefficient relating to one material characteristic in an eddy current field. The field equations are represented in terms of the potential field method (\(\varvec{T} - \psi \) method) and can be solved numerically by the nodal finite element method. We introduce a measurement as an additional condition and prove the existence and uniqueness of the weak solution. Further, we present an iteration algorithm for the recovery problem and validate its efficiency by two numerical experiments.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Sciences, Communication University of China, Beijing, 100024, People’s Republic of China

    Ran Wang, Tong Kang & Yanfang Wang

  2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, People’s Republic of China

    Yanfang Wang

Authors
  1. Ran Wang
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  2. Tong Kang
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  3. Yanfang Wang
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Corresponding author

Correspondence to Tong Kang.

Additional information

Communicated by Jorge X. Velasco.

This work was supported by National Science Foundation of China (41725017, 41590864, 11571352), National Basic Research Program of China under Grant number 2014CB845906. It was also partially supported by the CAS/CAFEA international partnership Program for creative research teams (No. KZZD-EW-TZ-19 and KZZD-EW-TZ-15).

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Wang, R., Kang, T. & Wang, Y. Boundary coefficient determination for an eddy current problem based on the potential field method. Comp. Appl. Math. 37, 3981–3994 (2018). https://doi.org/10.1007/s40314-017-0562-6

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  • DOI: https://doi.org/10.1007/s40314-017-0562-6

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