A Spectral Method For Solving Two Inverse Heat Conduction Problems

The inverse heat conduction problem is a class of classical inverse problem arising in the study of heat conduction phenomena.In this paper,the solution for two kinds of inverse heat conduction problems is studied.The first one is the inverse heat source problem in unbounded domain solved by the spectral and pseudospectral method of generalized Hermite function.We give the error estimate between the exact solution and the regularized solution and the stability estimate for the regularized solution.Theoretical analysis shows that by properly selecting the scaling factor in the generalized Hermite function,the number of the basis functions of the projection space can be significantly reduced,thus the computational efficiency can be improved.The second one is the two-dimensional reverse-time heat conduction problem solved by the Fourier spectral method and the SOR iterative technique.In the process of solving the direct problem by standard Galerkin method,the coefficient matrix can be sparse by selecting the basis functions appropriately.Then the elimination method is employed to considerably reduce the amount of the calculations in the process of solving the inverse problem.