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

Abstract

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