A numerical solution of the linear multidimensional unsteady inverse heat conduction problem with the boundary element method and the singular value decomposition

Lagier, Guy Laurent; Lemonnier, H.; Coutris, N.

doi:10.1016/j.ijthermalsci.2003.06.002

Cited by 17 publications

(12 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The unknown thermal coefficients on the mathematical model (i.e., thermal properties, boundary or initial conditions) that lead to an acceptable value for the aforementioned error function, based on the iterative regularization method, are the solution of the IHCP. In addit ion to textbooks [1,2] available in the literature, nu merous recent published researches have discussed the estimat ion of boundary conditions in IHCP [3][4][5][6][7][8][9][10][11][12]. Most of the previous work was restricted to problems with constant thermophysical properties.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for nonlinear inverse heat conduction problem

Qian¹,

Wang²

2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

View full text Add to dashboard Cite

Abstract-Inverse Heat Conduction Problems(IHCPs) have been extensi vely studied over the last 60 years. They have numerous applications in many branches of science and technol ogy.The problem consists in determining the temperature and heat flux at inaccessible parts of the boundary of a 2-or 3-di mension al body from correspondi ng data-called " Cauchy data" on accessible parts of the boundary. It is well-known that IHCPs are severely ill-posed which means that small perturbations in the data may cause extremely large errors in the soluti on. In this contri buti on, I present an anal ysis of numerical soluti on of nonlinear inverse heat conduction problem in a region wi th movi ng boundaries, a regul arizati on method is used to construct an algorithm for smoothing the experi mental data in a complication of the input data for the i nverse problem.

show abstract

Section: Introductionmentioning

confidence: 99%

A numerical method for nonlinear inverse heat conduction problem

Qian¹,

Wang²

2013

Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information

View full text Add to dashboard Cite

show abstract

“…) of surface heat flux is assumed to apply between time steps (Beck et al 1996;Lin et al 2004). Other approaches utilize Newton's method (Dorai and Tortorelli 1997), the Laplace transform technique (Monde et al 2003), singular value decomposition of an operator matrix (Shenefelt et al 2002;Lagier et al 2004), the boundary element method (Lesnic et al 1996) and the conjugate gradient method (Huang and Yeh 2002). These citations are only examples, as the literature on these methods and others is extensive.…”

Section: Introductionmentioning

confidence: 99%

An inverse method to estimate stem surface heat flux in wildland fires

Bova

Dickinson

2009

Int. J. Wildland Fire

View full text Add to dashboard Cite

Abstract. Models of wildland fire-induced stem heating and tissue necrosis require accurate estimates of inward heat flux at the bark surface. Thermocouple probes or heat flux sensors placed at a stem surface do not mimic the thermal response of tree bark to flames. We show that data from thin thermocouple probes inserted just below the bark can be used, by means of a one-dimensional inverse heat conduction method, to estimate net heat flux (inward minus outward heat flow) and temperature at the bark surface. Further, we estimate outward heat flux from emitted water vapor and bark surface re-radiation. Estimates of surface heat flux and temperature made by the inverse method confirm that surface-mounted heat flux sensors and thermocouple probes overestimate surface heat flux and temperature. As a demonstration of the utility of the method, we characterized uneven stem heating, due to leeward, flame-driven vortices, in a prescribed surface fire. Advantages of using an inverse method include lower cost, ease of multipoint measurements and negligible effects on the target stem. Drawbacks of the simple inverse model described herein include inability to estimate heat flux in very moist bark and uncertainty in estimates when extensive charring occurs.

show abstract

“…The unreasonable results of traditional numerical methods often occur in the inverse problems undergoing the measured and contaminated errors on the over-specified B.C.s because of the ill-posed behavior in the linear algebraic system [4,17]. Mathematically speaking, the influence matrix in the inverse problem is ill-posed since the solution is very sensitive to the given data.…”

Section: Introductionmentioning

confidence: 99%

“…Such a divergent problem could be avoided by using regularization methods [1,2,4,7,15,18,19,[21][22][23][24]. For examples, the truncated singular value decomposition technique (TSVD) [10,11,17,19], the zeroth order and first order techniques of Tikhonov regularization technique [1,2,9,12,13,19,20] have been applied to deal with divergent problems. The three techniques can obtain a convergence solution more precisely and reasonably.…”

Section: Introductionmentioning

confidence: 99%

“…The three techniques can obtain a convergence solution more precisely and reasonably. The numerical methods combined with the regularization techniques of the TSVD method and Tikhonov method, respectively [1,2,10,17,25], had been successfully applied to overcome the ill-posed problem of the Laplace equation. In this paper, the desingularized meshless method (DMM) in conjunction with the two regularization techniques is employed to solve the inverse problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques

et al. 2008

View full text Add to dashboard Cite

The desingularized meshless method (DMM) has been successfully used to solve boundary-value problems with specified boundary conditions (a direct problem) numerically. In this paper, the DMM is applied to deal with the problems with over-specified boundary conditions. The accompanied ill-posed problem in the inverse problem is remedied by using the Tikhonov regularization method and the truncated singular value decomposition method. The numerical evidences are given to verify the accuracy of the solutions after comparing with the results of analytical solutions through several numerical examples. The comparisons of results using Tikhonov method and truncated singular value decomposition method are also discussed in the examples.

show abstract

A numerical solution of the linear multidimensional unsteady inverse heat conduction problem with the boundary element method and the singular value decomposition

Cited by 17 publications

References 4 publications

A numerical method for nonlinear inverse heat conduction problem

A numerical method for nonlinear inverse heat conduction problem

An inverse method to estimate stem surface heat flux in wildland fires

Desingularized meshless method for solving Laplace equation with over-specified boundary conditions using regularization techniques

Contact Info

Product

Resources

About