# Crack detection using electrostatic measurements

Martin Brühl; Martin Hanke; Michael Pidcock

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 35, Issue: 3, page 595-605
- ISSN: 0764-583X

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topBrühl, Martin, Hanke, Martin, and Pidcock, Michael. "Crack detection using electrostatic measurements." ESAIM: Mathematical Modelling and Numerical Analysis 35.3 (2010): 595-605. <http://eudml.org/doc/197441>.

@article{Brühl2010,

abstract = {
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 the practical implementation of our algorithm
more computationally demanding.
},

author = {Brühl, Martin, Hanke, Martin, Pidcock, Michael},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Inverse boundary value problem; nondestructive testing; crack.; inverse boundary value problem; crack detection; Neumann-Dirichlet operators; factorization; practical implementation; algorithm},

language = {eng},

month = {3},

number = {3},

pages = {595-605},

publisher = {EDP Sciences},

title = {Crack detection using electrostatic measurements},

url = {http://eudml.org/doc/197441},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Brühl, Martin

AU - Hanke, Martin

AU - Pidcock, Michael

TI - Crack detection using electrostatic measurements

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 3

SP - 595

EP - 605

AB -
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 the practical implementation of our algorithm
more computationally demanding.

LA - eng

KW - Inverse boundary value problem; nondestructive testing; crack.; inverse boundary value problem; crack detection; Neumann-Dirichlet operators; factorization; practical implementation; algorithm

UR - http://eudml.org/doc/197441

ER -

## References

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- L. Mönch, On the numerical solution of the direct scattering problem for an open sound-hard arc. J. Comput. Appl. Math.71 (1996) 343-356.
- N. Nishimura and S. Kobayashi, A boundary integral equation method for an inverse problem related to crack detection. Internat. J. Numer. Methods Engrg.32 (1991) 1371-1387.
- F. Santosa and M. Vogelius, A computational algorithm to determine cracks from electrostatic boundary measurements. Internat. J. Engrg. Sci.29 (1991) 917-937.

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