A multi‐level adaptive solution strategy for 3D inverse problems in pool boiling

Purpose – The purpose of this paper is to present an efficient algorithm based on a multi‐level adaptive mesh refinement strategy for the solution of ill‐posed inverse heat conduction problems arising in pool boiling using few temperature observations.Design/methodology/approach – The stable solution of the inverse problem is obtained by applying the conjugate gradient method for the normal equation method together with a discrepancy stopping rule. The resulting three‐dimensional direct, adjoin and sensitivity problems are solved numerically by a space‐time finite element method. A multi‐level computational approach, which uses an a posteriori error estimator to adaptively refine the meshes on different levels, is proposed to speed up the entire inverse solution procedure.Findings – This systematic approach can efficiently solve the large‐scale inverse problem considered without losing necessary detail in the estimated quantities. It is shown that the choice of different termination parameters in the disc...