A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources

Karami, G.; Hematiyan, M. R.

doi:10.1002/(sici)1099-0887(200003)16:3<191::aid-cnm321>3.0.co;2-n

Cited by 16 publications

(6 citation statements)

References 12 publications

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“…Gallego and Suárez [3] proposed the solution of inverse potential fields using the BEM to identify the position and size of the unknown flaw. Karami and Hematiyan [4] emphasized the BEM to estimate the locations of multiple point heat sources in the two-dimensional (2D) case. Sumbatyan et al [5] developed an efficient algorithm in the framework of the scalar 2D anti-plane problem for a practical reconstruction in the elliptic void class.…”

Section: Introductionmentioning

confidence: 99%

Flaw identification for Laplace equation using the linear sampling method

Manshadi

Amiri

et al. 2017

Mathematics and Mechanics of Solids

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The present study aims to introduce the linear sampling method for cavity/inclusion detection in a two-dimensional Laplace problem by measuring data on the boundary. This method is categorized as a qualitative approach to image the geometrical features of unknown targets. There has been no specific attempt to apply this method to the identification of cavities/inclusions in the Laplace equation although it has been used in the context of inverse problems such as acoustics, electromagnetism and elastostatics. Therefore, the implementation of the linear sampling method, coupled with the finite element method, is emphasized in this study. A set of numerical simulations on two-dimensional problems is presented to highlight many effective features of the proposed qualitative identification method.

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Section: Introductionmentioning

confidence: 99%

Flaw identification for Laplace equation using the linear sampling method

Manshadi

Amiri

et al. 2017

Mathematics and Mechanics of Solids

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“…Several numerical methods have been proposed for the inverse heat source problem. The boundary element method (BEM), in conjunction with the regularization method, for recovering the solution has been developed in [6,7]. However, it required the evaluation of singular integrals.…”

Section: Introductionmentioning

confidence: 99%

A computational method for identifying a spacewise‐dependent heat source

Yan

Dou

2008

Numer Methods Biomed Eng

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SUMMARYIn this paper, we consider a finite difference approximation to an inverse problem of determining a spacewise-dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time.Since the resulting matrix equation is ill-conditioned, a regularized solution is obtained by employing the truncated singular value decomposition to solve the matrix equation arising from the finite difference method, with the optimal regularization parameter determined by the generalized cross-validation criterion. The effectiveness of the proposed numerical scheme is illustrated by several continuous and discontinuous numerical examples.

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“…Nevertheless, other functions and parameters can be estimated in the IHCP: heat transfer coefficients, static and moving heating sources, properties and initial conditions [2][3][4]. The IHCP is closely related to some inverse The future temperature methods, such as the FSM or the SSVD, are not explicitly formulated as a digital filter; nevertheless under the assumption of a linear problem, these methods can be expressed as digital filters.…”

Section: Introductionmentioning

confidence: 99%

“…For a better understanding of the little differences between estimations obtained by FSM and SSVD methods, the numerical simulations (Section 6) have been carried out using the same set of random errors. The first attempt to solve the inverse problem can be the identification of measured temperatures Y with the calculated temperatures T from the mathematical model given by Equation (4), so that the unknown vector q can be obtained from…”

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confidence: 99%

Filter digital form of two future temperature methods for the inverse heat conduction: A spectral comparison

Cabeza

García²,

Rodríguez

2008

Numer Methods Biomed Eng

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Sequential methods that use future times in order to solve an inverse heat conduction problem can be re-formulated as a sequential digital filter algorithm. The aim of this paper is to explore the filter effect of the function specification method and the truncated singular value decomposition method, in a sequential form. For this purpose, the power spectral densities of the corresponding filter coefficients are evaluated and it is shown that they act as band-pass filter. Three numerical tests with different frequency spectra are considered in order to solve a linear one-dimensional transient inverse problem. Furthermore, three models of crescent complexity are used in each method. It is shown that both methods provide similar results and in most cases, the optimum estimations require the same number of future times. As it is expected, similar estimations correspond to a similar band-pass filter. The effect of the number of future times, the influence of the frequency spectrum of the input and the complexity of the model used can be clearly interpreted in the spectral space. The most complex models act as a highly selective band-pass filter, but they require greater number of future times. 555 design problems, for example, the identification of the boundary shape of a domain subject to natural convection from temperature measurements on the other boundary [5]. The IHCP is a clear example of an ill-posed problem [1]. The main difficulty of this type of problem is the instability. From a mathematical point of view, the algebraic formulation of IHCP leads to an ill-conditioned problem, so that a small perturbation in the measured data (due to the unavoidable measurement errors) may cause great oscillations in the estimated function. This difficulty (from a physical point of view) is a consequence of the diffusive nature of heat flow, so that the thermal response at some distance of the boundary is damped and lagged with respect to the active input at the boundary [1]. In order to add stability at the solution of the inverse problem, many and different methods have been reported to solve IHCPs. Among the more versatile methods (applicable to solve multidimensional and non-linear IHCP) the following can be mentioned: Tikhonov regularization [6], iterative regularization [7], mollification [8] and the function specification method (FSM) [1]. The first two methods are considered as 'whole domain' because all the measured temperature data (N ) are used in order to estimate simultaneously all the components of the unknown input. In these methods, the sensitivity matrix can be of great dimensions (N × N ). In contrast, the last two methods are sequential. Therefore, only a small part of the available measurement is used in each step and only one component of the unknown input is estimated at each step. This fact can be an advantage in an online process. A considerable number of contributions have been published considering combinations, modifications and comparisons of the previous methods [9][10][11][12][13][14].Another ...

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A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources

Cited by 16 publications

References 12 publications

Flaw identification for Laplace equation using the linear sampling method

Flaw identification for Laplace equation using the linear sampling method

A computational method for identifying a spacewise‐dependent heat source

Filter digital form of two future temperature methods for the inverse heat conduction: A spectral comparison

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