A method of fundamental solutions for inverse heat conduction problems in an anisotropic medium

2007 ◽  
Vol 31 (1) ◽  
pp. 75-82 ◽  
Author(s):  
C.F. Dong ◽  
F.Y. Sun ◽  
B.Q. Meng
Keyword(s):  
Heat Conduction ◽  
Anisotropic Medium ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Inverse Heat Conduction ◽  
Inverse Heat Conduction Problems

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 A New Hybrid Method for Solving Inverse Heat Conduction Problems

2021 ◽  
Vol 15 ◽  
pp. 151-158
Author(s):  
M. R. Shahnazari ◽  
F. Roohi Shali ◽  
A. Saberi ◽  
M. H. Moosavi
Keyword(s):  
Heat Conduction ◽  
Inverse Problems ◽  
Regularization Parameter ◽  
Accurate Method ◽  
Fundamental Solutions ◽  
Industrial Applications ◽  
Inverse Heat Conduction ◽  
Constant Coefficients ◽  
Ill Posed ◽  
Inverse Heat Conduction Problems

Solving the inverse problems, especially in the field of heat transfer, is one of the challenges of engineering due to its importance in industrial applications. It is well-known that inverse heat conduction problems (IHCPs) are severely ill-posed, which means that small disturbances in the input may cause extremely large errors in the solution. This paper introduces an accurate method for solving inverse problems by combining Tikhonov's regularization and the genetic algorithm. Finding the regularization parameter as the decisive parameter is modelled by this method, a few sample problems were solved to investigate the efficiency and accuracy of the proposed method. A linear sum of fundamental solutions with unknown constant coefficients assumed as an approximated solution to the sample IHCP problem and collocation method is used to minimize residues in the collocation points. In this contribution, we use Morozov's discrepancy principle and Quasi-Optimality criterion for defining the objective function, which must be minimized to yield the value of the optimum regularization parameter.

Models and Methods of Semi-Infinite Optimization Inverse Heat-Conduction Problems

2006 ◽  
Vol 37 (3) ◽  
pp. 221-232 ◽  
Author(s):  
E. Ya. Rapoport ◽  
Yu. E. Pleshivtseva
Keyword(s):  
Heat Conduction ◽  
Inverse Heat Conduction ◽  
Inverse Heat Conduction Problems

Efficient Numerical Solution of Inverse Heat Conduction Problems

1995 ◽  
Author(s):  
Hans-Jürgen Reinhardt ◽  
Dinh Nho Hao
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Numerical Methods ◽  
Stationary Point ◽  
Forthcoming Paper ◽  
Inverse Heat Conduction ◽  
Piecewise Constant ◽  
Numerical Tests ◽  
Inverse Heat Conduction Problems ◽  
Special Case

Abstract In this contribution we propose new numerical methods for solving inverse heat conduction problems. The methods are constructed by considering the desired heat flux at the boundary as piecewise constant (in time) and then deriving an explicit expression for the solution of the equation for a stationary point of the minimizing functional. In a very special case the well-known Beck method is obtained. For the time being, numerical tests could not be included in this contribution but will be presented in a forthcoming paper.

An observer-based solution of inverse heat conduction problems

1990 ◽  
Vol 33 (7) ◽  
pp. 1545-1562 ◽  
Author(s):  
Wolfgang Marquardt ◽  
Hein Auracher
Keyword(s):  
Heat Conduction ◽  
Inverse Heat Conduction ◽  
Inverse Heat Conduction Problems
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