Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation

Tao Liu (), Di Ouyang, Lianjun Guo, Ruofeng Qiu, Yunfei Qi, Wu Xie, Qiang Ma and Chao Liu
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Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Di Ouyang: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Lianjun Guo: Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration, Qinhuangdao 066000, China
Ruofeng Qiu: Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration, Qinhuangdao 066000, China
Yunfei Qi: Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration, Qinhuangdao 066000, China
Wu Xie: Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration, Qinhuangdao 066000, China
Qiang Ma: Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
Chao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Mathematics, 2023, vol. 11, issue 13, 1-15

Abstract: This paper delves into a rapid and accurate numerical solution for the inverse problem of the nonlinear diffusion equation in the context of multiphase porous media flow. For the realization of this, the combination of the multigrid method with constraint data is utilized and investigated. Additionally, to address the ill-posedness of the inverse problem, the Tikhonov regularization is incorporated. Numerical results demonstrate the computational performance of this method. The proposed combination strategy displays remarkable capabilities in reducing noise, avoiding local minima, and accelerating convergence. Moreover, this combination method performs better than any one method used alone.

Keywords: inverse problem; nonlinear diffusion equation; multigrid method; constraint data; regularization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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