Determination of a time-dependent heat source from nonlocal boundary conditions

Hazanee, A.; Lesnic, D.

doi:10.1016/j.enganabound.2013.03.003

Cited by 21 publications

(14 citation statements)

References 10 publications

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“…As it happened previously with some of our investigations [13,14], we report that the secondorder Tikhonov regularization has produced more accurate results than the zeroth-or first-order regularization and therefore, only the numerical results obtained using the former regularization are illustrated in this section. A popular method for choosing the regularization parameter is the generalised cross-validation (GCV) criterion, which is based on minimising the following GCV function, [32]:…”

Section: Examplementioning

confidence: 82%

“…Inverse time-dependent source problems for the heat equation with local, nonlocal, integral or nonclassical (boundary) conditions have become the point of interest in many recent papers, [10,12,13,14,17,31,33], to name only a few. In the present paper, we consider yet another reconstruction of a time-dependent heat source from an integral over-determination measurement of the thermal energy of the system and a new dynamic-type boundary condition.…”

Section: Introductionmentioning

confidence: 99%

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An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

Hazanee

Lesnic

Ismailov

et al. 2015

Applied Mathematical Modelling

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This paper investigates the inverse problem of determining the time-dependent heat source and the temperature for the heat equation with a non-classical boundary and an integral over-determination conditions. The existence, uniqueness and continuous dependence upon the data of the classical solution of the inverse problem is shown by using the generalised Fourier method. Furthermore in the numerical process, the boundary element method (BEM) together with the second-order Tikhonov regularization is employed with the choice of regularization parameter based on the generalised cross-validation (GCV) criterion. Numerical results are presented and discussed.

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Section: Examplementioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

Hazanee

Lesnic

Ismailov

et al. 2015

Applied Mathematical Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

“…, that satisfies equations (2)- (4), (6) and (7). For the definition of the spaces involved, see [16].…”

Section: Inverse Problem Imentioning

confidence: 99%

“…While spacewise dependent perfusion coefficient identification in the transient bio-heat equation subjected to timeaveraging temperature measurement was investigated in [25] using the Crank-Nicolson FDM scheme combined with the first-order Tikhonov regularization method. On the other hand, time-dependent coefficient identification problems have been investigated recently, just to mention a few, the time-dependent inverse source identification problem [7,22,26] and the thermal conductivity/diffusivity identification problem [9,17] subjected to various kinds of overdetermination conditions.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous determination of time and space-dependent coefficients in a parabolic equation

Hussein

Lesnic

2016

Communications in Nonlinear Science and Numerical Simulation

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This paper investigates a couple of inverse problems of simultaneously determining time and space dependent coefficients in the parabolic heat equation using initial and boundary conditions of the direct problem and overdetermination conditions. The measurement data represented by these overdetermination conditions ensure that these inverse problems have unique solutions. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization method. The finite-difference method (FDM) is employed as a direct solver which is fed iteratively in a nonlinear minimization routine. Both exact and noisy data are inverted. Numerical results for a few benchmark test examples are presented, discussed and assessed with respect to the FDM mesh size discretisation, the level of noise with which the input data is contaminated, and the chosen regularization parameters.

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“…Methods of finding thermal conductivity have been studied by many researchers, as an example we refer to works [1][2][3][4][5]. However, when it comes to practical application of the developed methods, the new circumstances are found out that are not taken into account in the theoretical development of methods of calculation of thermal properties of materials.…”

Section: Introductionmentioning

confidence: 99%

An iterative method to calculate the thermal characteristics of the rock mass with inaccurate initial data

2016

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Abstract:The paper discusses the coefficient inverse problem for one-dimensional heat equation with inaccurate initial data. A conjugate difference problem is developed on difference level. The problem is solved by method of interval analysis. Condition of applicability of Thomas method and its computational convergence are obtained. Estimates of the interval width of solutions of difference problems and functions of Thomas method are also gained.

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Determination of a time-dependent heat source from nonlocal boundary conditions

Cited by 21 publications

References 10 publications

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

An inverse time-dependent source problem for the heat equation with a non-classical boundary condition

Simultaneous determination of time and space-dependent coefficients in a parabolic equation

An iterative method to calculate the thermal characteristics of the rock mass with inaccurate initial data

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