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A Posteriori Error Estimates and Adaptive Error Control for Permittivity Reconstruction in Conductive Media

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Gas Dynamics with Applications in Industry and Life Sciences (GKDLS 2021, GKDLS 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 429))

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Abstract

An inverse problem of reconstruction of the spatially distributed dielectric permittivity function in the Maxwell’s system is considered. The reconstruction method is based on the optimization approach to find stationary point of the Tikhonov functional. A posteriori estimates for the corresponding Tikhonov functional and for the reconstructed dielectric permittivity function are derived. Based on these estimates two adaptive conjugate gradient algorithms are formulated. Our numerical tests show feasibility of application of an adaptive optimization algorithm for reconstruction of dielectric permittivity function using anatomically realistic breast phantom of MRI database produced in University of Wisconsin [53].

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Acknowledgements

The research of both authors is supported by the Swedish Research Council grant VR 2018-03661. The research of L.B. is supported also by the sabbatical programme at the Faculty of Science, University of Gothenburg.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96, Gothenburg, Sweden

    L. Beilina & E. Lindström

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  1. L. Beilina
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Correspondence to L. Beilina .

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Editors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden

    Mohammad Asadzadeh

  2. Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden

    Larisa Beilina

  3. Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, Japan

    Shigeru Takata

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Beilina, L., Lindström, E. (2023). A Posteriori Error Estimates and Adaptive Error Control for Permittivity Reconstruction in Conductive Media. In: Asadzadeh, M., Beilina, L., Takata, S. (eds) Gas Dynamics with Applications in Industry and Life Sciences. GKDLS GKDLS 2021 2022. Springer Proceedings in Mathematics & Statistics, vol 429. Springer, Cham. https://doi.org/10.1007/978-3-031-35871-5_7

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