Volume 14, Issue 6
A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System

Int. J. Numer. Anal. Mod., 14 (2017), pp. 893-915.

Published online: 2017-10

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• Abstract

This paper studies a regularization approach for simultaneously reconstructing space-time dependent Robin coefficient $\gamma(\rm{x}, t)$ 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.

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

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@Article{IJNAM-14-893, author = {}, 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 = {2017}, volume = {14}, number = {6}, pages = {893--915}, abstract = {

This paper studies a regularization approach for simultaneously reconstructing space-time dependent Robin coefficient $\gamma(\rm{x}, t)$ 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/10486.html} }
TY - JOUR T1 - A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 893 EP - 915 PY - 2017 DA - 2017/10 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10486.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 $\gamma(\rm{x}, t)$ 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. (1970). 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. 14 (6). 893-915. doi:
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