The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity

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

doi:10.1016/j.compstruc.2014.01.007

Cited by 33 publications

(20 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It should be mentioned that the TSVD solution (35) can also be expressed analogously to the TRM and DSVD solutions given by equations (32) and (33), respectively, by defining the corresponding filter factors ϕ…”

Section: Svd-based Regularization Methodsmentioning

confidence: 99%

A numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticity

Marin

Karageorghis

Lesnic

2014

Numerical Methods Partial

View full text Add to dashboard Cite

We study the reconstruction of the missing thermal and mechanical data on an inaccessible part of the boundary in the case of two-dimensional linear isotropic thermoelastic materials from over-prescribed noisy measurements taken on the remaining accessible boundary part. This inverse problem is solved by employing the method of fundamental solutions together with the method of particular solutions. The stabilisation of this inverse problem is achieved by using several singular value decomposition (SVD)-based regularization methods, such as the Tikhonov regularization method [36], the damped SVD and the truncated SVD [37], whilst the optimal regularization parameter is selected according to the discrepancy principle [38], generalized cross-validation criterion [39] and Hansen's L-curve method [40].

show abstract

Section: Svd-based Regularization Methodsmentioning

confidence: 99%

A numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticity

Marin

Karageorghis

Lesnic

2014

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…The fundamental solution for tractions can be obtained by first calculating the fundamental solutions of stresses and then applying the definition of the traction vector as given by Equation

T_{ij} (boldy, boldx) = \frac{c_{1}}{r^{2}} ([], c_{2} ((), r_{, i} n_{j} (boldy) - r_{, j} n_{i} (boldy)) + r_{, k} n_{k} (boldy) ((), c_{2} δ_{ij} + 3 r_{, i} r_{, j})) .

In the traditional MFS , the displacements and tractions can be approximated by a linear combination of fundamental solutions with respect to different source points x as follows:

\begin{matrix} u_{i} (y^{m}) & = \sum_{n = 1}^{N} α_{j}^{n} U_{i j} (y^{m}, x^{n}) \\ = \sum_{n = 1}^{N} [α_{1}^{n} U_{i 1} (y^{m}, x^{n}) + α_{2}^{n} U_{i 2} (y^{m}, x^{n}) + α_{3}^{n} U_{i 3} (y^{m}, x^{n})] \end{matrix}

…”

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

View full text Add to dashboard Cite

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.

show abstract

“…A regularized MFS has been proposed by the authors for solving the problem given by equations (2.1), (2.2), (2.7), (2.8) and (2.12) in [22] and the problem given by equations (2.1), (2.2), (2.10)-(2.12) in [16] and it is the purpose of the present study to develop the same method for solving the new inverse problem given by equations (2.1), (2.2), (2.7)-(2.9). One can remark that both these inverse problems can also be solved iteratively by minimizing the least squares gap…”

Section: Mathematical Formulationmentioning

confidence: 99%

The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data

Marin

Karageorghis

Lesnic

et al. 2016

Inverse Problems in Science and Engineering

Self Cite

View full text Add to dashboard Cite

Abstract. An inverse problem in static thermo-elasticity is investigated. The aim is to reconstruct the unspecified boundary data, as well as the temperature and displacement inside a body from over-specified boundary data measured on an accessible portion of its boundary. The problem is linear but ill-posed. The uniqueness of the solution is established but the continuous dependence on the input data is violated. In order to reconstruct a stable and accurate solution, the method of fundamental solutions is combined with Tikhonov regularization where the regularization parameter is selected based on the L-curve criterion. Numerical results are presented in both two and three dimensions showing the feasibility and ease of implementation of the proposed technique.

show abstract

The method of fundamental solutions for an inverse boundary value problem in static thermo-elasticity

Cited by 33 publications

References 18 publications

A numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticity

A numerical study of the SVD–MFS solution of inverse boundary value problems in two‐dimensional steady‐state linear thermoelasticity

A meshless singular boundary method for three‐dimensional elasticity problems

The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data

Contact Info

Product

Resources

About