A sparse regularization approach to inverse heat source identification

Abstract

This paper proposes a new sparse regularization approach for both steady-state and transient heat source identification within the finite element (FE) framework. The whole work is mainly twofold. On the one hand, the sparse regularization is introduced to formulate heat source identification with the sparsity constraint that the heat sources are often spatially sparse and thereof, the FE heat source vector is a sparse vector. On the other hand, the alternating minimization algorithm is developed to get the solution. Particular attention is paid to the choice of the regularization parameter which controls the sparsity of the heat sources and to this end, an efficient threshold setting method is presented. Three numerical examples concerning one-dimensional steady-state, two- and three-dimensional transient heat source identification are studied to testify the feasibility, performance and robustness of the proposed approach for steady-state or transient, single or multiple heat source identification.