Two Numerical Methods For Inverse Heat Conduction Problem In Composite Materials

The inverse heat conduction problem (IHCP) is one of the hot topics at theforefront of the inverse problems of mathematical physics, and has important appli-cation backgrounds in many areas such as the steel production. The inverse heatconduction problem in multi-layer domain as a key sub-problem in the process ofsteel production, risk management and thermal materials designs, has importanttheoretical and practical values, it is necessary for us to investigate this kind ofproblem. In this thesis, we shall show that the inverse heat conduction problem incomposite materials is ill-posed in the sense that arbitrarily”small” diferences inthe data can induce arbitrarily”large” errors on the solution. Two feasible regular-ization methods, including Fourier truncation method and the dual least squaresmethod, are provided to obtain numerical solution. Also, some error estimatesbetween the regularized solutions and the exact solutions are given.This paper is organized as follows:Section1is a briefly introduction on the inverse problems and the two regular-ization methods (Fourier truncation method and dual least square method);in Section2, Fourier truncation method is used to solve the classical inverseheat conduction problem in multi-layer domain and the stability estimate is provedunder an a-priori conditions;in Section3, some knowledge about the Bessel function was represent as apreparation of Section4;in Section4, the dual least square method that based on the Shannon waveletsis applied to stabilize a radially symmetric inverse heat conduction problem in multi-layer domain. Also some error estimates are proved; Section5is a summary about this paper and an outlook on future work.