A Nonlinear Multigrid Method for the Parameter Identification Problem of Partial Differential Equations with Constraints
Tao Liu (liutao@neuq.edu.cn),
Jiayuan Yu,
Yuanjin Zheng,
Chao Liu,
Yanxiong Yang and
Yunfei Qi
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Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066000, China
Jiayuan Yu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066000, China
Yuanjin Zheng: School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore
Chao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066000, China
Yanxiong Yang: 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
Mathematics, 2022, vol. 10, issue 16, 1-12
Abstract:
In this paper, we consider the parameter identification problem of partial differential equations with constraints. A nonlinear multigrid method is introduced to the process of parameter inversion. By keeping the objective functions on coarse grids consistent with those on fine grids, the proposed method reduces the dimensions of objective functions enormously and mitigates the risk of trapping in local minima effectively. Furthermore, constraints significantly improve the convergence ability of the method. We performed the numerical simulation based on the porosity identification of elastic wave equations in the fluid-saturated porous media, which suggests that the nonlinear multigrid method with constraints decreases the computational expenditure, suppresses the noise, and improves the inversion results.
Keywords: inverse problem; parameter identification problem; partial differential equation; nonlinear multigrid method; constraints (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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