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Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data

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Abstract

We propose an efficient inverse solver for identifying the diffusion coefficient based on few random measurements which can be contaminated with noise. We focus mainly on problems involving solutions with steep heat gradients common with sudden changes in the temperature. Such steep gradients can be a major challenge for numerical solutions of the forward problem as they may involve intensive computations especially in the time domain. This intensity can easily render the computations prohibitive for the inverse problems that requires many repetitions of the forward solution. Compared to the literature, we propose to make such computations feasible by developing an iterative approach that is based on the partition of unity finite element method, hence, significantly reducing the computations intensity. The proposed approach inherits the flexibility of the finite element method in dealing with complicated geometries, which otherwise cannot be achieved using analytical solvers. The algorithm is evaluated using several test cases. The results show that the approach is robust and highly efficient even when the input data is contaminated with noise.

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Acknowledgements

Our research is supported by National Natural Science Foundation of China, No.51775270, and Jiangsu Innovation Program for Graduate Education, No.KYLX16_0314. Financial support provided by the project of Qatar National Research Fund under the contract NPRP11S-1220- 170112 is gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Jinhui Jiang

  2. School of Energy, Geoscience, Infrastructure and Society, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    M. Shadi Mohamed

  3. Department of Engineering, University of Durham, South Road, Durham, DH1 3LE, UK

    Mohammed Seaid

  4. Mechatronic Engineering College, Jinling Institute of Technology, Nanjing, 211169, China

    Hongqiu Li

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  1. Jinhui Jiang
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Jiang, J., Shadi Mohamed, M., Seaid, M. et al. Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data. Arch Appl Mech 91, 1623–1639 (2021). https://doi.org/10.1007/s00419-020-01844-7

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