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Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method

Author

Listed:
  • Tao Liu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
    School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore)

  • Zijian Ding

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Jiayuan Yu

    (School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Wenwen Zhang

    (School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore)

Abstract

This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples.

Suggested Citation

  • Tao Liu & Zijian Ding & Jiayuan Yu & Wenwen Zhang, 2023. "Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2642-:d:1167891
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    References listed on IDEAS

    as
    1. El Houcine Bergou & Youssef Diouane & Vyacheslav Kungurtsev, 2020. "Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 927-944, June.
    2. Damian Słota & Agata Chmielowska & Rafał Brociek & Marcin Szczygieł, 2020. "Application of the Homotopy Method for Fractional Inverse Stefan Problem," Energies, MDPI, vol. 13(20), pages 1-14, October.
    3. Hassan K. Ibrahim Al-Mahdawi & Hussein Alkattan & Mostafa Abotaleb & Ammar Kadi & El-Sayed M. El-kenawy, 2022. "Updating the Landweber Iteration Method for Solving Inverse Problems," Mathematics, MDPI, vol. 10(15), pages 1-13, August.
    Full references (including those not matched with items on IDEAS)

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