A sparse regularization approach to inverse heat source identification - Lu, Zhong-Rong; Pan, Tiancheng; Wang, Li (International journal of heat and mass transfer, 2019)
•A new sparse regularization approach is proposed for both location and strength identification of the heat sources.•The key idea resides at that the heat sources are always spatially sparse.•Numerical examples show that the sparse regularization indeed improves the robustness of heat source identification.•The present approach is found to perform superior to the Tikhonov regularization and the conjugate gradient method.•The proposed approach can identify the transient heat sources using only boundary data. 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.