Combination of multigrid with constraint data for inverse problem of nonlinear diffusion equation

Combination of multigrid with constraint data for inverse problem of nonlinear diffusion equation

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. Additiona...

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Bibliographic Details
Main Authors: Liu, Tao, Ouyang, Di, Guo, Lianjun, Qiu, Ruofeng, Qi, Yunfei, Xie, Wu, Ma, Qiang, Liu, Chao
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Inverse Problem
Nonlinear Diffusion Equation
Online Access:https://hdl.handle.net/10356/171720
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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