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M Mierzwiczak - One of the best experts on this subject based on the ideXlab platform.
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the singular boundary method for steady state nonlinear Heat Conduction Problem with temperature dependent thermal conductivity
International Journal of Heat and Mass Transfer, 2015Co-Authors: M Mierzwiczak, Zhuojia FuAbstract:Abstract This paper presents the singular boundary method for steady-state nonlinear Heat Conduction Problems. In the steady-state nonlinear Heat Conduction Problem, the Kirchhoff transformation is employed to remove the nonlinearity associated with the temperature dependence of the thermal conductivity. Then the transformed Laplace-type equation is investigated by the present singular boundary method with a simple iteration procedure. Finally, the temperature field is derived by the inverse Kirchhoff transformation. The present algorithm is verified on several examples involving various expressions of temperature dependent thermal conductivity and different computational domains. Numerical results show good accuracy and stability of the proposed strategy.
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the determination temperature dependent thermal conductivity as inverse steady Heat Conduction Problem
International Journal of Heat and Mass Transfer, 2011Co-Authors: M Mierzwiczak, Jan Adam KolodziejAbstract:The paper deals with the non-iterative inverse determination of the temperature-dependent thermal conductivity in 2-D steady-state Heat Conduction Problem. The thermal conductivity is modeled as a polynomial function of temperature with the unknown coefficients. The identification of the thermal conductivity is obtained by using the boundary data and additionally from the knowledge of temperature inside the domain. The method of fundamental solutions is used to solve the 2-D Heat Conduction Problem. The golden section search is used to find the optimal place for pseudo-boundary on which are placed the singularities in the frame of method of fundamental solutions.
Daniel Lesnic - One of the best experts on this subject based on the ideXlab platform.
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a boundary element method for a multi dimensional inverse Heat Conduction Problem
International Journal of Computer Mathematics, 2012Co-Authors: Phan Xuan Thanh, Daniel Lesnic, B T JohanssonAbstract:In this paper, we investigate a variational method for a multi-dimensional inverse Heat Conduction Problem in Lipschitz domains. We regularize the Problem by using the boundary element method coupled with the conjugate gradient method. We prove the convergence of this scheme with and without Tikhonov regularization. Numerical examples are given to show the efficiency of the scheme.
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a comparative study on applying the method of fundamental solutions to the backward Heat Conduction Problem
Mathematical and Computer Modelling, 2011Co-Authors: B T Johansson, Daniel Lesnic, Thomas ReeveAbstract:We investigate an application of the method of fundamental solutions (MFS) to the backward Heat Conduction Problem (BHCP). We extend the MFS in Johansson and Lesnic (2008) [5] and Johansson et al. (in press) [6] proposed for one and two-dimensional direct Heat Conduction Problems, respectively, with the sources placed outside the space domain of interest. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.
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an iterative boundary element method for solving the one dimensional backward Heat Conduction Problem
International Journal of Heat and Mass Transfer, 2001Co-Authors: N S Mera, Lionel Elliott, Derek B. Ingham, Daniel LesnicAbstract:Abstract In this paper, the iterative algorithm proposed by V.A. Kozlov and V.G. Maz'ya [Leningrad Math. J. 5 (1990) 1207–1228] is numerically implemented using the boundary element method (BEM) in order to solve the backward Heat Conduction Problem (BHCP). The convergence and the stability of the numerical method are investigated and a stopping criterion is proposed. The numerical results obtained confirm that the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data.
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the boundary element solution of the cauchy steady Heat Conduction Problem in an anisotropic medium
International Journal for Numerical Methods in Engineering, 2000Co-Authors: N S Mera, Lionel Elliott, Derek B. Ingham, Daniel LesnicAbstract:In this paper the iterative algorithm proposed by Kozlov et al. for the Cauchy Problem for the Laplace equation is extended in order to solve the Cauchy steady-state Heat Conduction Problem in an anisotropic medium. The iterative algorithm is numerically implemented using the boundary element method (BEM). The convergence and the stability of the numerical method, as well as various types of accuracy, convergence and stopping criteria, are investigated. The numerical results obtained confirm that provided an appropriate stopping regularization criterion is imposed, then the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularization criterion to cease the iterative process is proposed and the rate of convergence of the algorithm is improved by using various relaxation procedures between iterations. A new concept of a variable relaxation factor is proposed. Analytical formulae for the coefficients of the matrices resulting from the direct application of the BEM in an anisotropic medium are also presented. Copyright © 2000 John Wiley & Sons, Ltd.
Hong Chen - One of the best experts on this subject based on the ideXlab platform.
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a decentralized fuzzy inference method for the inverse geometry Heat Conduction Problem
Applied Thermal Engineering, 2016Co-Authors: Yanhao Li, Guangjun Wang, Hong Chen, Daqian ZhangAbstract:Abstract This paper studies an inverse internal geometry Problem with two-dimensional Heat Conduction system by using the boundary element method (BEM) and fuzzy inference method (FIM). BEM is utilized to solve the direct Heat Conduction Problem for the assumed inner shape in advance, and a set of fuzzy inference units is established to obtain a set of fuzzy inference components by the deviations between the computed temperature and measured temperature. Finally, the fuzzy inference components are weighted and synthesized to gain the compensations of inner shape. Numerical experiments are carried out to analyze the performance of two weighted ways, and the effects of initial guesses of inner geometry shape, the number of measured point and measurement errors on the inversion results are discussed respectively by comparing the inversion results of the conjugate gradient method (CGM). For the inverse geometry boundary Heat Conduction Problem researched by this paper, the results show that compared with the CGM, FIM can significantly reduce the dependence of the inversion results on the number of measured point and improve the anti-interference ability on measurement errors, which has better anti ill-posed characteristic.
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a decentralized fuzzy inference method for solving the two dimensional steady inverse Heat Conduction Problem of estimating boundary condition
International Journal of Heat and Mass Transfer, 2011Co-Authors: Guangjun Wang, Hong ChenAbstract:Abstract This paper addresses a new technique for solving the two-dimensional steady inverse Heat Conduction Problem, which named decentralized fuzzy inference (DFI) method. First of all, a group of decentralized fuzzy inference units are designed, and the fuzzy inference for each fuzzy inference unit is conducted which bases on the difference between the measured and the computed temperature at each measuring location. The computed temperatures are obtained by solving the direct Heat Conduction Problem with the finite difference method. And then, inference results of fuzzy inference units are weighted to yield compensation values of the unknown boundary temperatures. The unknown boundary temperatures are estimated by updating guess temperatures continuously with compensation values. Numerical experiments are carried out with different initial guesses, the number of measuring points and measurement errors. Comparing results of DFI method and Levenberg–Marquardt (L–M) method, we can conclude that DFI method is valid.
Chenghung Huang - One of the best experts on this subject based on the ideXlab platform.
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an inverse hyperbolic Heat Conduction Problem in estimating surface Heat flux by the conjugate gradient method
Journal of Physics D, 2006Co-Authors: Chenghung Huang, Hsin Hsien WuAbstract:In the present study an inverse hyperbolic Heat Conduction Problem is solved by the conjugate gradient method (CGM) in estimating the unknown boundary Heat flux based on the boundary temperature measurements. Results obtained in this inverse Problem will be justified based on the numerical experiments where three different Heat flux distributions are to be determined. Results show that the inverse solutions can always be obtained with any arbitrary initial guesses of the boundary Heat flux. Moreover, the drawbacks of the previous study for this similar inverse Problem, such as (1) the inverse solution has phase error and (2) the inverse solution is sensitive to measurement error, can be avoided in the present algorithm. Finally, it is concluded that accurate boundary Heat flux can be estimated in this study.
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a three dimensional inverse Heat Conduction Problem in estimating surface Heat flux by conjugate gradient method
International Journal of Heat and Mass Transfer, 1999Co-Authors: Chenghung Huang, Shao Pei WangAbstract:Abstract In the present study a three-dimensional (3-D) transient inverse Heat Conduction Problem is solved using the conjugate gradient method (CGM) and the general purpose commercial code CFX4.2-based inverse algorithm to estimate the unknown boundary Heat flux in any 3-D irregular domain. The advantage of calling CFX4.2 as a subroutine in the present inverse calculation lies in that many difficult but practical 3-D inverse Problems that can be solved under this construction. Results obtained by using the conjugate gradient method to solve these 3-D inverse Problems are justified based on the numerical experiments. It is concluded that accurate boundary fluxes can be estimated by the CGM except for the final time. The reason and improvement of this singularity are addressed. Finally, the effects of the measurement errors on the inverse solutions are discussed.
N S Mera - One of the best experts on this subject based on the ideXlab platform.
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the method of fundamental solutions for the backward Heat Conduction Problem
Inverse Problems in Science and Engineering, 2005Co-Authors: N S MeraAbstract:In this article a meshless numerical scheme for solving the backward Heat Conduction Problem (BHCP) is proposed. The numerical solution is developed by using the fundamental solution of the Heat equation as a basis function. The standard Tikhonov regularization technique and the L-curve method are adopted for solving the resultant ill-conditioned system of linear algebraic equations. The convergence and the stability of the method are investigated for a severe test example, hence revealing the computational performance and limitations of the method proposed. Numerical results are presented for bo th the one-dimensional and the two-dimensional backward Heat Conduction Problems.
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an iterative algorithm for the backward Heat Conduction Problem based on variable relaxation factors
Inverse Problems in Engineering, 2002Co-Authors: M Jourhmane, N S MeraAbstract:In this paper, an iterative algorithm is proposed for solving the backward Heat Conduction Problem (BHCP). The algorithm is based on allowing variable relaxation factors for an iterative algorithm proposed by Kozlov and Maz'ya [1]. The convergence of the relaxation algorithm is analysed both theoretically and numerically. The boundary element method (BEM) is used to implement numerically the algorithm and to show that the ill-posed BHCP is regularized by using an appropriate stopping criterion.
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an iterative boundary element method for solving the one dimensional backward Heat Conduction Problem
International Journal of Heat and Mass Transfer, 2001Co-Authors: N S Mera, Lionel Elliott, Derek B. Ingham, Daniel LesnicAbstract:Abstract In this paper, the iterative algorithm proposed by V.A. Kozlov and V.G. Maz'ya [Leningrad Math. J. 5 (1990) 1207–1228] is numerically implemented using the boundary element method (BEM) in order to solve the backward Heat Conduction Problem (BHCP). The convergence and the stability of the numerical method are investigated and a stopping criterion is proposed. The numerical results obtained confirm that the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data.
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the boundary element solution of the cauchy steady Heat Conduction Problem in an anisotropic medium
International Journal for Numerical Methods in Engineering, 2000Co-Authors: N S Mera, Lionel Elliott, Derek B. Ingham, Daniel LesnicAbstract:In this paper the iterative algorithm proposed by Kozlov et al. for the Cauchy Problem for the Laplace equation is extended in order to solve the Cauchy steady-state Heat Conduction Problem in an anisotropic medium. The iterative algorithm is numerically implemented using the boundary element method (BEM). The convergence and the stability of the numerical method, as well as various types of accuracy, convergence and stopping criteria, are investigated. The numerical results obtained confirm that provided an appropriate stopping regularization criterion is imposed, then the iterative BEM produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data. An efficient stopping regularization criterion to cease the iterative process is proposed and the rate of convergence of the algorithm is improved by using various relaxation procedures between iterations. A new concept of a variable relaxation factor is proposed. Analytical formulae for the coefficients of the matrices resulting from the direct application of the BEM in an anisotropic medium are also presented. Copyright © 2000 John Wiley & Sons, Ltd.
