A meshless method to the solution of an ill-posed problem

2016 ◽  
Vol 24 (5) ◽  
Author(s):  
Malihe Rostamian ◽  
Alimardan Shahrezaee
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Numerical Approximation ◽  
Heat Conduction Problem ◽  
Noisy Data ◽  
Numerical Approach ◽  
Inverse Heat Conduction Problem ◽  
Tikhonov Regularization Method ◽  
Inverse Heat Conduction ◽  
Ill Posed

AbstractIn this paper, we consider an inverse heat conduction problem (IHCP). First, the existence, uniqueness and unstability solution of the inverse problem will be studied. Due to the ill-posedness of the inverse problem, we propose a meshless numerical approach based on basis function to solve this problem in the presence of noisy data. The Tikhonov regularization method with generalized discrepancy principle is applied to obtain a stable numerical approximation to the solution. The effectiveness of the algorithm is illustrated by some numerical examples.

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.

scholarly journals A Mollification Regularization Method for a Fractional-Diffusion Inverse Heat Conduction Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zhi-Liang Deng ◽  
Xiao-Mei Yang ◽  
Xiao-Li Feng
Keyword(s):  
Regularization Method ◽  
Heat Conduction Problem ◽  
A Priori ◽  
Dirichlet Kernel ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Linear Diffusion ◽  
Ill Posed ◽  
Transient Data ◽  
Parameter Choice Rules

The ill-posed problem of attempting to recover the temperature functions from one measured transient data temperature at some interior point of a one-dimensional semi-infinite conductor when the governing linear diffusion equation is of fractional type is discussed. A simple regularization method based on Dirichlet kernel mollification techniques is introduced. We also proposea priorianda posterioriparameter choice rules and get the corresponding error estimate between the exact solution and its regularized approximation. Moreover, a numerical example is provided to verify our theoretical results.

An Initial Value Approach to the Inverse Heat Conduction Problem

1986 ◽  
Vol 108 (2) ◽  
pp. 248-256 ◽  
Author(s):  
E. Hensel ◽  
R. G. Hills
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Noisy Data ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Initial Value ◽  
Surface Conditions ◽  
One Dimensional ◽  
The One

The one-dimensional linear inverse problem of heat conduction is considered. An initial value technique is developed which solves the inverse problem without need for iteration. Simultaneous estimates of the surface temperature and heat flux histories are obtained from measurements taken at a subsurface location. Past and future measurement times are inherently used in the analysis. The tradeoff that exists between resolution and variance of the estimates of the surface conditions is discussed quantitatively. A stabilizing matrix is introduced to the analysis, and its effect on the resolution and variance of the estimates is quantified. The technique is applied to “exact” and “noisy” numerically simulated experimental data. Results are presented which indicate the technique is capable of handling both exact and noisy data.

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.

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.

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