A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System
Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 6 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10486
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 6 : pp. 893–915
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Simultaneous identification numerical reconstruction Robin coefficient and heat flux Tikhonov regularization FEM MCGM.