Volume 15, Issue 3
A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System

Int. J. Numer. Anal. Mod., 15 (2018), pp. 428-451.

Published online: 2018-03

Cited by

Export citation
• Abstract

This paper studies a regularization approach for simultaneously reconstructing space-time dependent Robin coefficient $γ(\rm x, t)$ and heat flux $q(\rm x, t)$. The differentiability results and adjoint systems are established. A standard finite element method (FEM) is employed to discretize the constrained optimization problem which is reduced to a sequence of unconstrained optimization problem by adding regularization terms. We propose an improved algorithm for the introduced problem based on modified conjugate gradient method (MCGM) for quadratic minimization. Numerical experiments present the efficiency, accuracy, and robustness of the proposed algorithm.

• Keywords

Simultaneous identification, Numerical reconstruction, Robin coefficient and heat flux, Tikhonov regularization, FEM, MCGM.

65M30, 65M32, 65M12, 65M60, 35K10

Talaat.2008@yahoo.com (Talaat Abdelhamid)

rl.chen@siat.ac.cn (Rongliang Chen)

• BibTex
• RIS
• TXT
@Article{IJNAM-15-428, author = {Talaat and Abdelhamid and Talaat.2008@yahoo.com and 7976 and School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China and Talaat Abdelhamid and Xiaomao and Deng and and 7977 and Physics and Mathematical Engineering Department, Faculty of Electronic Engineering, Menoufiya University, Menouf 32952, Egypt and Xiaomao Deng and Rongliang and Chen and rl.chen@siat.ac.cn and 13680 and Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China and Rongliang Chen}, title = {A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {15}, number = {3}, pages = {428--451}, abstract = {

This paper studies a regularization approach for simultaneously reconstructing space-time dependent Robin coefficient $γ(\rm x, t)$ and heat flux $q(\rm x, t)$. The differentiability results and adjoint systems are established. A standard finite element method (FEM) is employed to discretize the constrained optimization problem which is reduced to a sequence of unconstrained optimization problem by adding regularization terms. We propose an improved algorithm for the introduced problem based on modified conjugate gradient method (MCGM) for quadratic minimization. Numerical experiments present the efficiency, accuracy, and robustness of the proposed algorithm.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12524.html} }
TY - JOUR T1 - A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System AU - Abdelhamid , Talaat AU - Deng , Xiaomao AU - Chen , Rongliang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 428 EP - 451 PY - 2018 DA - 2018/03 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/12524.html KW - Simultaneous identification, Numerical reconstruction, Robin coefficient and heat flux, Tikhonov regularization, FEM, MCGM. AB -

This paper studies a regularization approach for simultaneously reconstructing space-time dependent Robin coefficient $γ(\rm x, t)$ and heat flux $q(\rm x, t)$. The differentiability results and adjoint systems are established. A standard finite element method (FEM) is employed to discretize the constrained optimization problem which is reduced to a sequence of unconstrained optimization problem by adding regularization terms. We propose an improved algorithm for the introduced problem based on modified conjugate gradient method (MCGM) for quadratic minimization. Numerical experiments present the efficiency, accuracy, and robustness of the proposed algorithm.

Talaat Abdelhamid, Xiaomao Deng & Rongliang Chen. (2020). A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System. International Journal of Numerical Analysis and Modeling. 15 (3). 428-451. doi:
Copy to clipboard
The citation has been copied to your clipboard