A Regularization Method For A Class Of Three-dimensional Reverse-time Heat Conduction Problems

This paper studies the numerical solution of a class of three-dimensional heat conduction problems.First,based on the finite-difference time discretization,com-bined with the Galerkin method to carry out finite element discretization of the space,a class of three-dimensional heat conduction equations is numerically solved.The three-dimensional thermoelastic equation was analyzed,and the stress and s-train state of the rectangular cross-section beam was analyzed based on the ISO-834 fire heating standard.Through numerical experiments,the structural changes of the beam within 4000 seconds of heating were observed,and the fire resistance perfor-mance was determined according to the failure criterion.Aiming at the corresponding inverse problem,the corresponding relationship between the temperature field at time T and the initial temperature field is estab-lished by the method of separating variables,the inversion equation is given,and the local stability of the inverse problem is proved under certain a priori assumption-s.In order to overcome the ill-posedness of solving the inverse problem,Tikhonov regularization and final value data perturbation regularization methods are used to invert the initial temperature field,and the effectiveness of the algorithm is verified by numerical experiments.