A domain decomposition method for the stable analysis of inverse nonlinear transient heat conduction problems

A method for solving nonlinear transient inverse heat conduction problems is presented. To overcome the nonlinearity of the problem, not only the time domain is divided into several sub-domains, but also the geometrical domain. By using an inverse method, the unknown variables are determined in each sub-domain. The finite element method (FEM) is used for the sensitivity analyses in the sub-domains. The ill-posedness of the inverse problem in each sub-domain is much less than that corresponding to the original domain and hence the inverse problem is solved efficiently in each sub-domain. Three nonlinear transient problems are analyzed by both the method presented in this paper and the conventional method. According to the results obtained, it is shown that the proposed domain decomposition method (DDM) is more stable, accurate and faster than the conventional method with a single domain.