The Application Of Two Kinds Of Regularization Method In The Two-dimensional Inverse Heat Conduction Problem

This paper mainly discusses two kinds of di?erent regularization method which areused to solve the two-dimensional inverse heat conduction problem with non-homogeneousterms.At the beginning, the paper brie?y introduces the ill-posed two-dimensional in-verse heat conduction problem and its research and development at home and abroad.In the second chapter, we prove the ill-posedness of the two-dimensional inverse heat con-duction problem with non-homogeneous terms by operator semigroup, then two kindsof regularization method are introduced for the problem: the regularization methodbased on Tikhonov method and the quasi-boundary value regularization method. In thethird chapter, we solve the two-dimensional inverse heat conduction problem with non-homogeneous terms by Tikhonov regularization method. In the SOR iteration processof solving regularization solution an explicit three layers di?erence scheme is used re-peatedly, so the program takes a long time but the numerical precision is relatively high.In the fourth chapter, we solve the two-dimensional inverse heat conduction problemwith non-homogeneous terms by the quasi-boundary value regularization method. Thismethod is simple and the program takes for a relatively short time, but comparing withthe first regularization method the numerical precision is relatively low. In this paperthe regularization parameter is selected by prior method. The relationship between thenumerical precision and regularization parameters are discussed. The numerical experi-ments indicate that the two regularization methods are quite e?ective.