A meshless singular boundary method for three-dimensional inverse heat conduction problems in general anisotropic media

Gu, Yan; Chen, Wen; Zhang, Chuanzeng; He, Xiaoqiao

doi:10.1016/j.ijheatmasstransfer.2015.01.003

Cited by 47 publications

(20 citation statements)

References 40 publications

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“…The OIF concept is first proposed in Chen et al [3], where an inverse interpolation technique is developed with using the set of sample points placed inside the domain. In recent research the SBM is successfully applied to potential [7], heat conduction [8], acoustic stokes flow [9], and biharmonic [10] problems.…”

Section: Introductionmentioning

confidence: 99%

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

Gnitko

Degtyariov

Karaiev

et al. 2019

Boundary Elements and Other Mesh Reduction Methods XLII

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A new numerical approach is proposed to address problems of free liquid vibrations in axisymmetric compound rigid shells using a singular boundary method. The liquid is supposed to be perfect and incompressible, and its flow is irrotational so the liquid velocity can be presented as a potential gradient. The approximation of a small fluid surface elevation is used, and the free surface function is presented as a sum of the fluid-filled shell height and the small elevation function. A series expansion of the potential function about stationary states is used. To find the stationary states, an eigenvalue problem is formulated. Eigenvalues and eigenvectors are obtained using the singular boundary method with the origin intensity factor as the singular integral over the singular boundary element. The numerical results for free vibration analysis of cylindrical shells, obtained by singular boundary method and direct boundary element methods, are compared. Different compound rigid shells are considered in numerical simulations of free liquid vibrations.

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Section: Introductionmentioning

confidence: 99%

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

Gnitko

Degtyariov

Karaiev

et al. 2019

Boundary Elements and Other Mesh Reduction Methods XLII

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show abstract

“…Another effective method, finite element methods, is also widely used for the numerical solution, see [24,25]. Another popular method for the direct and inverse heat conduction problems is the singular boundary method, we can see [26][27][28][29][30] for further reading.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Filtering the Noise in the Heat Conduction Problem

et al. 2019

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In this paper, we give an effective numerical method for the heat conduction problem connected with the Laplace equation. Through the use of a single-layer potential approach to the solution, we get the boundary integral equation about the density function. In order to deal with the weakly singular kernel of the integral equation, we give the projection method to deal with this part, i.e., using the Lagrange trigonometric polynomials basis to give an approximation of the density function. Although the problems under investigation are well-posed, herein the Tikhonov regularization method is not used to regularize the aforementioned direct problem with noisy data, but to filter out the noise in the corresponding perturbed data. Finally, the effectiveness of the proposed method is demonstrated using a few examples, including a boundary condition with a jump discontinuity and a boundary condition with a corner. Whilst a comparative study with the method of fundamental solutions (MFS) is also given.

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“…The method belongs to the family of meshless boundary collocation methods [3][4][5][6][7][8] and can be viewed as one kind of modified method of fundamental solutions (MFS) [9][10][11][12][13][14]. The method overcomes the fictitious boundary issue [15,16] associated with the traditional MFS while retaining the merits of the latter of being truly meshless, mathematically simple and easy-to-program. Prior to this study, the RMM has been successfully tried for 2D and 3D problems in potential theory [17], linear elasticity [18] and inverse problems [2].…”

Section: Introductionmentioning

confidence: 99%

Fast-multipole accelerated regularized meshless method for large-scale isotropic heat conduction problems

Wang

Chen

2016

International Journal of Heat and Mass Transfer

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A meshless singular boundary method for three-dimensional inverse heat conduction problems in general anisotropic media

Cited by 47 publications

References 40 publications

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

Singular Boundary Method in a Free Vibration Analysis of Compound Liquid-Filled Shells

A Numerical Method for Filtering the Noise in the Heat Conduction Problem

Fast-multipole accelerated regularized meshless method for large-scale isotropic heat conduction problems

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