Regularized MFS solution of inverse boundary value problems in three-dimensional steady-state linear thermoelasticity

Marin, Liviu; Karageorghis, Andréas; Lesnic, D.

doi:10.1016/j.ijsolstr.2016.03.013

Cited by 27 publications

(7 citation statements)

References 20 publications

(12 reference statements)

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“…;Feng Li and Chen (2014);Marin, Karageorghis and Lesnic (2016);Li, Lee, Huang et al (2017)]). For efficient use of the TSVD method, a suitable criterion for neglecting some smallest singular values should be employed.…”

mentioning

confidence: 99%

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Hematiyan¹,

Arezou²,

Dezfouli³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

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In this paper, some remarks for more efficient analysis of two-dimensional elastostatic problems using the method of fundamental solutions are made. First, the effects of the distance between pseudo and main boundaries on the solution are investigated and by a numerical study a lower bound for the distance of each source point to the main boundary is suggested. In some cases, the resulting system of equations becomes ill-conditioned for which, the truncated singular value decomposition with a criterion based on the accuracy of the imposition of boundary conditions is used. Moreover, a procedure for normalizing the shear modulus is presented that significantly reduces the condition number of the system of equations. By solving two example problems with stress concentration, the effectiveness of the proposed methods is demonstrated.

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mentioning

confidence: 99%

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Hematiyan¹,

Arezou²,

Dezfouli³

et al. 2019

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

show abstract

“…In recent years, there has been an increasing amount of literature on inverse problems (IPs) related to the classic thermoelastic system, e.g. [6,8,34,43,7,42,26,3,41,24,19,37,25,38,36,15,14]. These inverse problems in thermoelasticity addressed so far in the literature are mainly related to boundary data reconstruction [6,8,34,20,24,19,25,14], shape optimization problems, detection of flaws (e.g.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems

Maes

Bockstal

2022

Journal of Inverse and Ill-Posed Problems

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We study the uniqueness of some inverse source problems arising in thermoelastic models of type-III. We suppose that the source terms can be decomposed as a product of a time dependent and a space dependent function, i.e. g ⁢ ( t ) ⁢ 𝐟 ⁢ ( 𝐱 ) {g(t)\mathbf{f}(\mathbf{x})} for the load source and g ⁢ ( t ) ⁢ f ⁢ ( 𝐱 ) {g(t)f(\mathbf{x})} for the heat source. In the first inverse source problem, the source 𝐟 ⁢ ( 𝐱 ) {\mathbf{f}(\mathbf{x})} has to be determined from the final in time measurement of the displacement 𝐮 ⁢ ( 𝐱 , T ) {\mathbf{u}(\mathbf{x},T)} , or from the time-average measurement ∫ 0 T 𝐮 ⁢ ( 𝐱 , t ) ⁢ d t {\int_{0}^{T}\mathbf{u}(\mathbf{x},t)\,\mathrm{d}t} . In the second inverse source problem, the source f ⁢ ( 𝐱 ) {f(\mathbf{x})} has to be determined from the time-average measurement of the temperature ∫ 0 T θ ⁢ ( 𝐱 , t ) ⁢ d t {\int_{0}^{T}\theta(\mathbf{x},t)\,\mathrm{d}t} . We show the uniqueness of a solution to these problems under suitable assumptions on the function g ⁢ ( t ) {g(t)} . Moreover, we provide some examples showing the necessity of these assumptions. Finally, we conclude the article by studying two combined problems of determining both sources.

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“…The method won the favor of many researchers in engineering and science due to its advantage of high accuracy for many engineering applications [7,[9][10][11][12][13]. The classical MFS approach, however, produces dense and non-symmetric matrix of algebraic equations that requires memory and other operators to compute the unknown coefficients [14][15][16][17][18]. This makes the method limited to solving small-scale problems with thousands of degrees of freedom for a long time [7,[19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

Gu¹,

Fan²,

Fu³

2021

AAMM

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A localized version of the method of fundamental solution (LMFS) is devised in this paper for the numerical solutions of three-dimensional (3D) elasticity problems. The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation. Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations. Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies. The advantages, disadvantages and potential applications of the proposed method, as compared with the classical MFS and boundary element method (BEM), are discussed.

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Regularized MFS solution of inverse boundary value problems in three-dimensional steady-state linear thermoelasticity

Cited by 27 publications

References 20 publications

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Some Remarks on the Method of Fundamental Solutions for Two-Dimensional Elasticity

Uniqueness for inverse source problems of determining a space-dependent source in thermoelastic systems

Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

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