A method of fundamental solutions for the radially symmetric inverse heat conduction problem

2012 ◽  
Vol 39 (7) ◽  
pp. 887-895 ◽  
Author(s):  
B. Tomas Johansson ◽  
Daniel Lesnic ◽  
Thomas Reeve
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Fundamental Solutions ◽  
Inverse Heat Conduction Problem ◽  
Method Of Fundamental Solutions ◽  
Inverse Heat Conduction

METHOD OF FUNDAMENTAL SOLUTION FOR AN INVERSE HEAT CONDUCTION PROBLEM WITH VARIABLE COEFFICIENTS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341009 ◽  
Author(s):  
MING LI ◽  
XIANG-TUAN XIONG ◽  
YAN LI
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Fundamental Solutions ◽  
Variable Coefficients ◽  
Inverse Heat Conduction Problem ◽  
Method Of Fundamental Solutions ◽  
Inverse Heat Conduction ◽  
Modified Method ◽  
On Line ◽  
Ill Posed

In this paper, we consider an inverse heat conduction problem with variable coefficient a(t). In many practical situations such as an on-line testing, we cannot know the initial condition for example because we have to estimate the problem for the heat process which was already started. Based on the method of fundamental solutions, we give a numerical scheme for solving the reconstruction problem. Since the governing equation contains variable coefficients, modified method of fundamental solutions was used to solve this kind of ill-posed problems. Some numerical examples are given for verifying the efficiency and accuracy of the presented method.

scholarly journals Wavelet regularization for an inverse heat conduction problem

2003 ◽  
Vol 288 (1) ◽  
pp. 212-222 ◽  
Author(s):  
Chu-Li Fu ◽  
You-Bin Zhu ◽  
Chun-Yu Qiu
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Wavelet Regularization

Iterative methods for an inverse heat conduction problem

2001 ◽  
Vol 9 (4) ◽  
Author(s):  
G. Bastay ◽  
V.A. Kozlov ◽  
B.O. Turesson
Keyword(s):  
Heat Conduction ◽  
Iterative Methods ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction

scholarly journals A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Arghand ◽  
Majid Amirfakhrian
Keyword(s):  
Heat Conduction ◽  
Fundamental Solution ◽  
Meshless Method ◽  
Heat Conduction Problem ◽  
Regularization Parameter ◽  
Linear Equations ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Radial Basis ◽  
The Stability

We propose a new meshless method to solve a backward inverse heat conduction problem. The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution. Since the coefficients matrix is ill-conditioned, the Tikhonov regularization (TR) method is employed to solve the resulted system of linear equations. Also, the generalized cross-validation (GCV) criterion is applied to choose a regularization parameter. A test problem demonstrates the stability, accuracy, and efficiency of the proposed method.

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