Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (1): 187-200.

Previous Articles     Next Articles

Numerical Solution of the Three-Dimensional Inverse Heat Conduction Problems

Qingchun Meng1,2,Lei Zhang1,*()   

  1. 1 Department of Mathematical Sciences, Heilongjiang University, Harbin 150080
    2 Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Lviv, Ukraine 79013
  • Received:2021-01-11 Online:2022-02-26 Published:2022-02-23
  • Contact: Lei Zhang E-mail:zhanglei@hlju.edu.cn
  • Supported by:
    the NSFC(11871198);the NSFC(11801116);the Fundamental Research Funds for the Universities of Heilongjiang Province-Youth Innovation Team(RCYJTD201804);the Fundamental Research Funds for the Central Universities(3072020CFT2401)

Abstract:

In this paper, we consider the numerical solution of a three-dimensional inverse heat conduction problem. Based on the finite difference and the finite element method, the stiffness matrix and load vector are derived to solve the heat conduction problem. We use the variable separation method to establish the corresponding relationship between the temperature field at time T and the initial temperature field for the inverse problem. The inversion formulation is obtained. The local stability for the inverse problems is proved under certain priori assumptions. To overcome the ill-posedness for solving the inverse problem, we used the Tikhonov regularization and perturbation regularization method to reconstruct the initial temperature field. We verified the effectiveness of the algorithm through several numerical experiments.

Key words: 3-D inverse heat conduction problem, Finite element, Ill-posedness, Regularization method

CLC Number: 

  • O241.8
Trendmd