A New Method for Simultaneously Reconstructing the Space-Time Dependent Robin Coefficient and Heat Flux in a Parabolic System
Talaat Abdelhamid ,
Xiaomao Deng and
Rongliang Chen
Int. J. Numer. Anal. Mod., 14 (2017), pp. 893-915
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.
