Une méthode inverse à régularisation évanescente

Cimetière, Alain; Delvare, Franck; Pons, Frédéric

doi:10.1016/s1620-7742(00)01236-8

Cited by 13 publications

(29 citation statements)

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“…So then an iterative regularizing method is introduced to solve it. This method is a generalization of the inverse technique introduced by Cimetière et al [8,9] to solve the Cauchy problem for the Laplace equation. It can be considered as an iterative Tikhonov-type method.…”

Section: The Evanescent Regularization Methodsmentioning

confidence: 99%

“…In order to solve Cauchy problems for elliptic equations, many regularization methods have been introduced. The references [1,5,8,9,11,12,14,20,21,23,25,26] propose different methods of solving the Cauchy problem for the Laplace equation. References [2,3,13,22,23,27,28,29,30,31,32,33,34,35,36,37,38,40,41] deal with the Cauchy problem in linear elasticity.…”

Section: Introductionmentioning

confidence: 99%

“…References [2,3,13,22,23,27,28,29,30,31,32,33,34,35,36,37,38,40,41] deal with the Cauchy problem in linear elasticity. These methods can be classified as Tikhonov type methods [15,22,27,29,33,34,35,38,39,40,41], quasi-reversibility type methods [5,21,25], iterative methods [1,2,3,8,9,11,12,13,14,15,20,23,26,28,32,36,37],... Quasi reversibility methods and Tikhonov regularization methods present the advantage of leading to well posed problems after mod...…”

Section: Introductionmentioning

confidence: 99%

“…Some iterative methods are based on the use of a sequence of well-posed problems and others on the minimization of an energy-like functional. Numerical algorithms are implemented using different numerical methods, such as the finite element method (FEM) [1,2,3,5,8,9,11,13,27,38], the boundary element method (BEM) [12,14,20,22,26,23,28,29,30,31,32,33,36,37,40,41], the finite difference method [21] or meshless methods [34,35]. Some papers present comparisons between different numerical methods [10,31,37].…”

Section: Introductionmentioning

confidence: 99%

“…Some papers present comparisons between different numerical methods [10,31,37]. In previous works [8,9,12] a somewhat different resolution approach was first introduced in [8] for the Cauchy problem associated with the Laplace equation. This approach reduced the resolution of the Cauchy problem to the resolution of a sequence of optimization problems under equality constraints.…”

Section: Introductionmentioning

confidence: 99%

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An iterative method for the Cauchy problem in linear elasticity with fading regularization effect

Delvare¹,

Cimetière²,

Hanus³

et al. 2010

Computer Methods in Applied Mechanics and Engineering

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In this paper, an iterative method for solving the Cauchy problem in linear elasticity is introduced. This problem consists in recovering missing data (displacements and forces) on some parts of a domain boundary from the knowledge of overspecified data (displacements and forces) on the remaining parts. The algorithm reads as a least square fitting of the given data, with a regularization term whose effect fades as the iterations go on. So the algorithm converges to the solution of the Cauchy problem. Numerical simulations using the finite element method highlight the algorithm's efficiency, accuracy, robustness to noisy data as well as its ability to deblur noisy data.

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Section: The Evanescent Regularization Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An iterative method for the Cauchy problem in linear elasticity with fading regularization effect

Delvare¹,

Cimetière²,

Hanus³

et al. 2010

Computer Methods in Applied Mechanics and Engineering

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Fading regularization FEM algorithms for the Cauchy problem associated with the two‐dimensional biharmonic equation

Boukraa

Amdouni

Delvare

2022

Math Methods in App Sciences

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In this paper, we use the fading regularization method to solve a biharmonic inverse problem, represented by the Cauchy problem. Two formulations are studied and implemented numerically using a finite element method (FEM).We present numerical reconstructions of the missing data on the inaccessible part of the boundary from the knowledge of over-prescribed noisy data for both smooth and piecewise smooth two-dimensional geometries. Numerical examples validate the convergence, stability and efficiency of the proposed numerical algorithm, as well as its capability to deblur the noisy data.

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The Steklov‐Poincaré technique for data completion: Preconditioning and filtering

Ferrier

Kadri²,

Gosselet

2018

Numerical Meth Engineering

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Summary This paper presents a study of primal and dual Steklov‐Poincaré approaches for the identification of unknown boundary conditions of elliptic problems. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Different preconditioning and acceleration strategies are evaluated. We show that costless filtering of the solution is possible by postprocessing Ritz elements. Assessments are provided on a 3D mechanical problem.

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Une méthode inverse à régularisation évanescente

Cited by 13 publications

References 0 publications

An iterative method for the Cauchy problem in linear elasticity with fading regularization effect

An iterative method for the Cauchy problem in linear elasticity with fading regularization effect

Fading regularization FEM algorithms for the Cauchy problem associated with the two‐dimensional biharmonic equation

The Steklov‐Poincaré technique for data completion: Preconditioning and filtering

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