scholarly journals An inverse problem in estimating the time dependent source term and initial temperature simultaneously by the polynomial regression and conjugate gradient method

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3507-3516
Author(s):  
Arzu Coşkun
Keyword(s):  
Source Term ◽  
Initial Temperature ◽  
Polynomial Regression ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Necessary Condition ◽  
Inverse Heat Conduction ◽  
Control Framework ◽  
Ill Posed ◽  
The Stability

From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be effective in dealing with these problems. However, they require to find the gradient information. This idea has been employed in this research. We derive the gradient of Tikhonov functional and establish the stability of the minimizer from the necessary condition. The stability and effectiveness of evolutionary algorithm are presented for various test examples.

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.

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 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.

Numerical solution of two-dimensional radially symmetric inverse heat conduction problem

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Zhi Qian ◽  
Benny Y. C. Hon ◽  
Xiang Tuan Xiong
Keyword(s):  
Heat Conduction ◽  
Numerical Solution ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Convergence Error ◽  
Regularization Techniques ◽  
Ill Posed

AbstractWe investigate a two-dimensional radially symmetric inverse heat conduction problem, which is ill-posed in the sense that the solution does not depend continuously on input data. By generalizing the idea of kernel approximation, we devise a modified kernel in the frequency domain to reconstruct a numerical solution for the inverse heat conduction problem from the given noisy data. For the stability of the numerical approximation, we develop seven regularization techniques with some stability and convergence error estimates to reconstruct the unknown solution. Numerical experiments illustrate that the proposed numerical algorithm with regularization techniques provides a feasible and effective approximation to the solution of the inverse and ill-posed problem.

Solving an Inverse Heat Conduction Problem by a “Method of Lines”

1997 ◽  
Vol 119 (3) ◽  
pp. 406-412 ◽  
Author(s):  
L. Elde´n
Keyword(s):  
Heat Conduction ◽  
Heat Equation ◽  
Heat Conduction Problem ◽  
Time Derivative ◽  
Method Of Lines ◽  
Inverse Heat Conduction Problem ◽  
Heat Conducting ◽  
Inverse Heat Conduction ◽  
Use Of Time ◽  
Ill Posed

We consider a Cauchy problem for the heat equation in the quarter plane, where data are given at x = 1 and a solution is sought in the interval 0 < x < 1. This inverse heat conduction problem is a model of a situation where one wants to determine the surface temperature given measurements inside a heat-conducting body. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In an earlier paper we showed that replacement of the time derivative by a difference stabilizes the problem. In this paper we investigate the use of time differencing combined with a “method of lines” for solving numerically the initial value problem in the space variable. We discuss the numerical stability of this procedure, and we show that, in most cases, a usual explicit (e.g., Runge-Kutta) method can be used efficiently and stably. Numerical examples are given. The approach of this paper is proposed as an alternative way of implementing space-marching methods for the sideways heat equation.

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