Inverse heat conduction problems with boundary and final time measured output data

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights • Multi-dimensional space-dependent sources are reconstructed from boundary data. • Iterative regularization methods are developed. • Convergence and stability of numerical results are thoroughly investigated.

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“…Step 4 Solve the direct well-posed problem given by the equations (19) with f = d k , to determine Kd k defined by (18). Set…”

Section: The Conjugate Gradient Methodsmentioning

confidence: 99%

“…The one-dimensional case has been discussed in detail elsewhere, [17,18], and therefore it will not be considered herein. The two-dimensional case when Ω is a bounded planar domain reflects more the typical properties of the general inverse and ill-posed source problem.…”

Section: Numerical Discretisationmentioning

confidence: 99%

Identification of a multi-dimensional space-dependent heat source from boundary data

Hussein

Lesnic

Johansson

et al. 2018

Applied Mathematical Modelling

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“…Zheng and Yin [6] have studied the optimal time for the time optimal control problem governed by an internally controlled semi-linear heat equation. In [7][8][9], the inverse problems with different controls and cost functions have been investigated.…”

Section: Introductionmentioning

confidence: 99%

“…) in(8) and the functional Lv in(9). Let π (v, v) be a continuous symmetric bilinear coercive form and Lv be a continuous linear form.…”

mentioning

confidence: 99%

Identification of the initial temperature from the given temperature data at the left end of a rod

Saraç

Şener

2019

Applied Mathematics and Nonlinear Sciences

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This study aims to investigate the problem of determining the unknown initial temperature in a variable coefficient heat equation. We obtain the existence and uniqueness of the solution of the optimal control problem considered under some conditions. Using the adjoint problem approach, we get the Frechet differential of the cost functional. We construct a minimizing sequence and give the convergence rate of this sequence. Also, we test the theoretical results in a numerical example by using the MAPLE® program.

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“…See [22,23,24,25] for some papers on inverse heat conduction problems. Since the problem is not well-posed, to overcome the instability problem, one possible approach is to record the temperature history at more locations than the number of unknowns in the algebraic equations to be solved.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of 1D inverse heat conduction problems using overdetermined RBF-MLPG method

Shirzadi¹

2013

Communications in Numerical Analysis

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This paper proposes a numerical method to deal with the one-dimensional inverse heat conduction problem (IHCP). The initial temperature, a condition on an accessible part of the boundary and an additional temperature measurements in time at an arbitrary location in the domain are known, and it is required to determine the temperature and the heat flux on the remaining part of the boundary. Due to the missing boundary condition, the solution of this problem does not depend continuously on the data and therefore its numerical solution requires special care especially when noise is present in the measured data. In the proposed method, the time variable is eliminated by using finite differences approximation. The method uses a weak formulation of the problem to enjoy the stability condition. To avoid the numerical integration on the whole domain, the weak form equations are constructed on local subdomains. The approximate solution is assumed to be a linear combination of Multi Quadric (MQ) radial basis function (RBF) constructed on nodal points in the domain and on the boundary. Since the problem is known to be ill-posed, Thikhonov regularization strategy is employed to solve effectively the discrete ill-posed resultant linear system.

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Inverse heat conduction problems with boundary and final time measured output data

Cited by 24 publications

References 11 publications

Identification of a multi-dimensional space-dependent heat source from boundary data

Identification of a multi-dimensional space-dependent heat source from boundary data

Identification of the initial temperature from the given temperature data at the left end of a rod

Numerical simulations of 1D inverse heat conduction problems using overdetermined RBF-MLPG method

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