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 spacetime dependent Robin coefficient γ(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.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Talaat.2008@yahoo.com (Talaat Abdelhamid)

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

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