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

Talaat Abdelhamid, Xiaomao Deng & Rongliang Chen

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

Published online: 2018-03

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  • 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.

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Talaat.2008@yahoo.com (Talaat Abdelhamid)

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

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-15-428, author = {Abdelhamid , TalaatDeng , Xiaomao and Chen , Rongliang}, 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.

Abdelhamid , TalaatDeng , Xiaomao and Chen , Rongliang. (2018). 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:
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