Identification of time-dependent coefficients of heat transfer by the method of suboptimal stage-by-stage optimization

Borukhov, V. T.; Kostyukova, O. I.

doi:10.1016/j.ijheatmasstransfer.2012.12.029

Cited by 8 publications

(9 citation statements)

References 22 publications

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“…This problem is solved by a high-order compact finite difference method in [29]. The interested reader can see [1,2] for more research works on this problem. In this paper we introduce a new direct computational method to solve the inverse problem (1)- (5).…”

Section: A Brief Review Of Other Methods Existing In the Literaturementioning

confidence: 99%

Numerical solution of an inverse reaction–diffusion problem via collocation method based on radial basis functions

Parzlivand

Shahrezaee

2015

Applied Mathematical Modelling

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Please cite this article as: F. Parzlivand, A.M. Shahrezaee, Numerical solution of an inverse reaction-diffusion problem via collocation method based on radial basis functions, Appl. Math. Modelling (2014), doi: http://dx. Abstract.In this paper, a numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. This method is a combination of collocation method and radial basis functions. The operational matrix of derivative for radial basis functions is introduced and the new computational technique is used for this purpose. The operational matrix of derivative is utilized to reduce the problem to a set of algebraic equations. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.

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Section: A Brief Review Of Other Methods Existing In the Literaturementioning

confidence: 99%

Numerical solution of an inverse reaction–diffusion problem via collocation method based on radial basis functions

Parzlivand

Shahrezaee

2015

Applied Mathematical Modelling

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“…3. The second specific feature of the proposed approach is that the problem of reconstructing the heat flux q(x 0 , t), t ∈ [t 0 , t * ], is solved by the SSO method [18,19]. The essence and advantages of the method are described in Sect.…”

Section: б и б л и о т е к а б г у и рmentioning

confidence: 99%

“…To solve problem (11), we apply a method of a stage-by-stage optimization. The idea of the method is identical to that of the method described in [17][18][19]. The essence of the method consists in the reduction of the filtering procedure over the entire time interval t ∈ [t 0 , t * ] to the consecutive solution of p filtering problems on small time intervals t ∈ [τ j , τ j+1 ], j = 0, 1, ..., p − 1, where τ j = t 0 + jLΔt, is a time instant from the set {t i , i = 0, 1, ..., M } ⊂ [t 0 , t * ], L > 0, p > 0 are integers.…”

Section: б и б л и о т е к а б г у и рmentioning

confidence: 99%

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Reconstruction of the Surface Heat Flux for a Quasi-linear System of the Hyperbolic Type Heat-Conduction Equations

Borukhov

Kostyukova

2015

Communications in Computer and Information Science

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The problem of the identification of the surface heat flux for a quasi-linear system of the hyperbolic type heat-conduction equations is studied. An approach is proposed based on the stage-by-stage suboptimal optimization of the cost functional and input data filtering using the HuberTikhonov functional. Results are presented for the numerical modeling of the identification problem in conditions of both standard noisy data and noise emissions.

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“…The numerical solution of inverse Stefan problems based on the method of fundamental solutions has been investigated in [13,14]. The determination of time-dependent thermal coefficients was solved using the method of suboptimal stage-by-stage optimization in [3]. The heat equation with an unknown time-dependent thermal diffusivity or heat source in a domain with a free boundary has been investigated in [11] and [17], respectively.…”

Section: Introductionmentioning

confidence: 99%

Time-Dependent Reaction Coefficient Identification Problems with a Free Boundary

Huntul

Lesnic

2019

International Journal for Computational Methods in Engineering

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The determination of time-dependent reaction coefficients in free boundary heat transfer problems is, for the first time, numerically investigated. The additional data which provides a unique solution is given by the Stefan boundary condition and the heat moments. The finite difference method with the Crank-Nicolson scheme combined with a regularized nonlinear optimization are employed. The resulting nonlinear system of equations is solved numerically using the MATLAB toolbox routine lsqnonlin for minimizing the Tikhonov regularization functional. A discussion of the choice of regularization parameters is provided. Numerical results are presented and discussed.

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Identification of time-dependent coefficients of heat transfer by the method of suboptimal stage-by-stage optimization

Cited by 8 publications

References 22 publications

Numerical solution of an inverse reaction–diffusion problem via collocation method based on radial basis functions

Numerical solution of an inverse reaction–diffusion problem via collocation method based on radial basis functions

Reconstruction of the Surface Heat Flux for a Quasi-linear System of the Hyperbolic Type Heat-Conduction Equations

Time-Dependent Reaction Coefficient Identification Problems with a Free Boundary

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