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

Volume 14, Issue 6

Talaat Abdelhamid, Xiaomao Deng & Rongliang Chen

DOI:

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 spacetime dependent Robin coefficient ϒ(x, t) and heat flux q(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.

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@Article{IJNAM-14-893, author = {Talaat Abdelhamid, Xiaomao Deng 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 = {2017}, volume = {14}, number = {6}, pages = {893--915}, abstract = {This paper studies a regularization approach for simultaneously reconstructing spacetime dependent Robin coefficient ϒ(x, t) and heat flux q(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 AU - Talaat Abdelhamid, Xiaomao Deng & Rongliang Chen 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 KW - numerical reconstruction KW - Robin coefficient and heat flux KW - Tikhonov regularization KW - FEM KW - MCGM AB - This paper studies a regularization approach for simultaneously reconstructing spacetime dependent Robin coefficient ϒ(x, t) and heat flux q(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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