A method of fundamental solutions for the radially symmetric inverse heat conduction problem

Johansson, Björn; Lesnic, D.; Reeve, Thomas

doi:10.1016/j.icheatmasstransfer.2012.05.011

Cited by 20 publications

(6 citation statements)

References 20 publications

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“…These source points are either pre‐assigned or taken to be part of the unknowns of the problem along with the coefficients

{α_{j}^{n}}_{n = 1}^{N}

. In either case, the unknowns are determined so that the approximations and satisfy, in some sense, the boundary conditions and as close as possible . In the early applications of the MFS, the locations of the source points were determined by a nonlinear system of the equations that can be solved using a nonlinear least‐squares minimization software.…”

Section: Mfs Formulation For 3d Elasticity Problemsmentioning

confidence: 99%

A meshless singular boundary method for three‐dimensional elasticity problems

Chen

Gao

et al. 2016

Numerical Meth Engineering

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SUMMARYThis study documents the first attempt to extend the singular boundary method, a novel meshless boundary collocation method, for the solution of 3D elasticity problems. The singular boundary method involves a coupling between the regularized BEM and the method of fundamental solutions. The main idea here is to fully inherit the dimensionality and stability advantages of the former and the meshless and integrationfree attributes of the later. This makes it particularly attractive for problems in complex geometries and three dimensions. Four benchmark 3D problems in linear elasticity are well studied to demonstrate the feasibility and accuracy of the proposed method. The advantages, disadvantages, and potential applications of the proposed method, as compared with the FEM, BEM, and method of fundamental solutions, are also examined and discussed.

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“…These source points are either pre‐assigned or taken to be part of the unknowns of the problem along with the coefficients

{α_{j}^{n}}_{n = 1}^{N}

Section: Mfs Formulation For 3d Elasticity Problemsmentioning

confidence: 99%

A meshless singular boundary method for three‐dimensional elasticity problems

Chen

Gao

et al. 2016

Numerical Meth Engineering

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“…Inverse heat conduction problem has a broad application prospect in nondestructive testing, geometry optimization, aerospace engineering, power engineering, mechanical engineering, construction engineering, biological engineering, metallurgical engineering, materials processing, biomedical and food engineering, and other fields [1][2][3][4][5][6][7][8][9][10][11][12]. Focusing on this problem, domestic and foreign scholars have done a lot of research.…”

Section: Introductionmentioning

confidence: 99%

Solution to Two‐Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

Wang

Zhang

Sun

et al. 2017

Mathematical Problems in Engineering

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The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points' number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.

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“…This IHCP equation is analyzed in the literature. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] Hetmaniok et al [1] applied the homotopy perturbation method for the solution of inverse heat conduction problem. Moreover, Slota [2] implemented homotopy perturbation method for the solution of one phase.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of the imprecisely defined inverse heat conduction problem

2015

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This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solution process, double parametric forms of fuzzy numbers are used with the variational iteration method (VIM). This problem first computes the uncertain temperature distribution in the domain. Next, when the uncertain temperature measurements in the domain are known, the functions describing the uncertain temperature and heat flux on the boundary are reconstructed. Related example problems are solved using the present procedure. We have also compared the present results with those in [Inf. Sci. (2008) 178 1917] along with homotopy perturbation method (HPM) and [Int. Commun. Heat Mass Transfer (2012) 39 30] in the special cases to demonstrate the validity and applicability.

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A method of fundamental solutions for the radially symmetric inverse heat conduction problem

Cited by 20 publications

References 20 publications

A meshless singular boundary method for three‐dimensional elasticity problems

A meshless singular boundary method for three‐dimensional elasticity problems

Solution to Two‐Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

Numerical solution of the imprecisely defined inverse heat conduction problem

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