A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat conduction problem

2007 ◽  
Vol 75 (3-4) ◽  
pp. 97-112 ◽  
Author(s):  
Wei Cheng ◽  
Chu-Li Fu ◽  
Zhi Qian
Keyword(s):  
Heat Conduction ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Three Dimensional ◽  
Inverse Heat Conduction Problem ◽  
Tikhonov Regularization Method ◽  
Spherically Symmetric ◽  
Inverse Heat Conduction

scholarly journals Optimal Tikhonov approximation for a sideways parabolic equation

2005 ◽  
Vol 2005 (8) ◽  
pp. 1221-1237 ◽  
Author(s):  
Chu-Li Fu ◽  
Hong-Fang Li ◽  
Xiang-Tuan Xiong ◽  
Peng Fu
Keyword(s):  
Heat Conduction ◽  
Parabolic Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Tikhonov Regularization Method ◽  
Inverse Heat Conduction ◽  
Convection Term ◽  
Ill Posed

We consider an inverse heat conduction problem with convection term which appears in some applied subjects. This problem is ill posed in the sense that the solution (if it exists) does not depend continuously on the data. A generalized Tikhonov regularization method for this problem is given, which realizes the best possible accuracy.

Analysis of Order of the Sequential Regularization Solutions of Inverse Heat Conduction Problems

1989 ◽  
Vol 111 (2) ◽  
pp. 218-224 ◽  
Author(s):  
E. P. Scott ◽  
J. V. Beck
Keyword(s):  
Heat Conduction ◽  
Regularization Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Inverse Heat Conduction Problem ◽  
Regularization Methods ◽  
Inverse Heat Conduction ◽  
Random Errors ◽  
Internal Temperature ◽  
Inverse Heat Conduction Problems

Various methods have been proposed to solve the inverse heat conduction problem of determining a boundary condition at the surface of a body from discrete internal temperature measurements. These include function specification and regularization methods. This paper investigates the various components of the regularization method using the sequential regularization method proposed by Beck and Murio (1986). Specifically, the effects of the regularization order and the influence of the regularization parameter are analyzed. It is shown that as the order of regularization increases, the bias errors decrease and the variance increases. Comparatively, the zeroth regularization has higher bias errors and the second-order regularization is more sensitive to random errors. As the regularization parameter decreases, the sensitivity of the estimator to random errors is shown to increase; on the other hand, the bias errors are shown to decrease.

Sign in / Sign up

Export Citation Format

Share Document