A survey of applications of the MFS to inverse problems

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

doi:10.1080/17415977.2011.551830

Cited by 199 publications

(76 citation statements)

References 100 publications

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“…An extensive survey of the applications of the MFS to inverse problems is provided in [20]. It appears that the MFS was used for the first time for the solution of inverse geometric problems in linear elasticity by Alves and Martins [3], who adapted to the detection of rigid inclusions or cavities in an elastic body the method of Kirsch and Kress [25].…”

Section: Introductionmentioning

confidence: 99%

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

Karageorghis

Lesnic

Marin

2016

Computers & Structures

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We investigate the numerical reconstruction of smooth star-shaped voids (rigid inclusions and cavities) which are compactly contained in a three-dimensional isotropic linear elastic medium from a single set of Cauchy data (i.e. nondestructive boundary displacement and traction measurements) on the accessible outer boundary. This inverse geometric problem in three-dimensional elasticity is approximated using the method of fundamental solutions (MFS). The parameters describing the boundary of the unknown void, its centre, and the contraction and dilation factors employed for selecting the fictitious surfaces where the MFS sources are to be positioned, are taken as unknowns of the problem. In this way, the original inverse geometric problem is reduced to finding the minimum of a nonlinear least-squares functional that measures the difference between the given and computed data, penalized with respect to both the MFS constants and the derivative of the radial coordinates describing the position of the star-shaped void. The interior source points are anchored and move with the void during the iterative reconstruction procedure. The feasibility of this new method is illustrated in several numerical examples.

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Section: Introductionmentioning

confidence: 99%

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

Karageorghis

Lesnic

Marin

2016

Computers & Structures

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“…In particular, as stated in [11], the MFS is meshless in the sense that only a collection of points is required for the discretization of the problem under investigation. Unlike the BEM, no potentially troublesome integration is required in the MFS.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, like the BEM it can easily deal with infinite domains by incorporating the behaviour of the solution of the problem at infinity into the fundamental solution of the governing equation. Because of its advantages, the MFS has been used extensively over the last decade for the solution of inverse problems [11]. In the particular problem under investigation because of the way the particular solution is derived it appears natural to use the MFS.…”

Section: Introductionmentioning

confidence: 99%

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

Karageorghis¹,

Lesnic²,

Marin³

2014

Computers & Structures

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The inverse problem of coupled static thermo-elasticity in which one has to determine the thermo-elastic stress state in a body from displacements and temperature given on a subset of the boundary is considered.A regularized method of fundamental solutions is employed in order to find a stable numerical solution to this ill-posed, but linear coupled inverse problem. The choice of the regularization parameter is based on the L-curve criterion. Numerical results are presented and discussed.

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“…The method of fundamental solution (MFS) is a meshless Trefftz method which has, in recent years, been extensively used for the numerical solution of inverse geometric problems [14]. More specifically, it has been frequently used for inverse geometric problems in acoustics, see e.g.…”

Section: Introductionmentioning

confidence: 99%

The MFS for the identification of a sound-soft interior acoustic scatterer

Karageorghis

Lesnic

Marin

2017

Engineering Analysis with Boundary Elements

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Abstract. We employ the method of fundamental solutions (MFS) for detecting a sound-soft scatterer surrounding a host acoustic homogeneous medium due to a given point source inside it. The measurements are taken inside the medium and, in addition, are contaminated with noise. The MFS discretization yields a nonlinear constrained regularized minimization problem which is solved using standard software. The results of several numerical experiments are presented and discussed.

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A survey of applications of the MFS to inverse problems

Cited by 199 publications

References 100 publications

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

The method of fundamental solutions for three-dimensional inverse geometric elasticity problems

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

The MFS for the identification of a sound-soft interior acoustic scatterer

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