Abstract
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem as a constrained optimization problem with total variation regularization. The existence and stability are proved for the solution to the optimization problem. The finite element method is employed to discretize the optimization problem. The gradient Lipschitz property of the objective functional is established for the discrete optimization problem. We propose a novel modification to the traditional alternating direction method of multipliers, and prove the convergence of the modified algorithm. Finally, we show some numerical experiments to illustrate the efficiency of the proposed method.
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The work was supported by National Key R &D Program of China 2019YFA0709600, 2019YFA0709602 and by NSFC under the grant 11871300.
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Chen, J., Long, Z. An Iterative Method for the Inverse Eddy Current Problem with Total Variation Regularization. J Sci Comput 99, 38 (2024). https://doi.org/10.1007/s10915-024-02501-9
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DOI: https://doi.org/10.1007/s10915-024-02501-9
Keywords
- Inverse eddy current problem
- Total variation regularization
- Alternating direction method of multipliers
- Convergence analysis