Based On The Integral Equation Inverse Heat Conduction Problems Numerical Methods

The aim of this paper is to present an inversion scheme for 2-D backward heat problem in general 2-D domain D (?) R~2. Such problems arise in many engineering areas such as archaeology and reaction-diffusion process. The physical description is to determine the initial field distribution from its final measurement given at some time T > 0 .Mathematically, this problem belongs to the category of inverse problems for parabolic equations. This paper study the numerical method of backward heat problem in general 2-D domain. Firstly based on the potential theory, we transform the solution of backward heat equations into that of equivalent integral equations, then an improved Tikhonov regularization method can be used to solve the problem. Finally, numerical performances are given to show the validity of this regularizing scheme.This paper is organized for four chapters. In chapter 1 we introduce some knowledge of heat conduction problem and inverse heat conduction problem; In chapter 2 we present the fundamental definitions for ill-posed problem, Tikhonov regularization method, improved Tikhonov regularization method and regularizing parameter selection; The mathematical model of 2-D heat conduction problem is established in chapter 3, and propose the numerical method based on the integral equation; In chapter 4 we analyze the ill-posed property for 2-D backward heat conduction problem , based on the integral equation's regularizing method, we solute the equation and give the numerical simulation for the algorithm.