Displaying similar documents to “Crack detection using electrostatic measurements”

Crack detection using electrostatic measurements

Martin Brühl, Martin Hanke, Michael Pidcock (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes...

Computation of the demagnetizing potential in micromagnetics using a coupled finite and infinite elements method

François Alouges (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is devoted to the practical computation of the magnetic potential induced by a distribution of magnetization in the theory of micromagnetics. The problem turns out to be a coupling of an interior and an exterior problem. The aim of this work is to describe a complete method that mixes the approaches of Ying [12] and Goldstein [6] which consists in constructing a mesh for the exterior domain composed of homothetic layers. It has the advantage of being well suited for catching...

On the Schwarz algorithms for the elliptic exterior boundary value problems

Faker Ben Belgacem, Miche Fournié, Nabil Gmati, Faten Jelassi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical...

Diffusion and propagation problems in some ramified domains with a fractal boundary

Yves Achdou, Christophe Sabot, Nicoletta Tchou (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of ℝ 2 with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for...