Crack detection using electrostatic measurements

Martin Brühl; Martin Hanke; Michael Pidcock

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

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

Abstract

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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 the practical implementation of our algorithm more computationally demanding.

How to cite

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Brühl, Martin, Hanke, Martin, and Pidcock, Michael. "Crack detection using electrostatic measurements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.3 (2001): 595-605. <http://eudml.org/doc/194064>.

@article{Brühl2001,
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 - Modélisation Mathématique et Analyse Numérique},
keywords = {inverse boundary value problem; nondestructive testing; crack; crack detection; Neumann-Dirichlet operators; factorization; practical implementation; algorithm},
language = {eng},
number = {3},
pages = {595-605},
publisher = {EDP-Sciences},
title = {Crack detection using electrostatic measurements},
url = {http://eudml.org/doc/194064},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Brühl, Martin
AU - Hanke, Martin
AU - Pidcock, Michael
TI - Crack detection using electrostatic measurements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
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; crack detection; Neumann-Dirichlet operators; factorization; practical implementation; algorithm
UR - http://eudml.org/doc/194064
ER -

References

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  1. [1] G. Alessandrini and A. Diaz Valenzuela, Unique determination of multiple cracks by two measurements. SIAM J. Control Optim. 34 (1996) 913–921. Zbl0864.35115
  2. [2] M. Brühl, Explicit characterization of inclusions in electrical impedance tomography. SIAM J. Math. Anal. 32 (2001) 1327–1341. Zbl0980.35170
  3. [3] M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Problems 16 (2000) 1029–1042. Zbl0955.35076
  4. [4] K. Bryan and M. Vogelius, A computational algorithm to determine crack locations from electrostatic boundary measurements. The case of multiple cracks. Internat. J. Engrg. Sci. 32 (1994) 579–603. Zbl0924.73179
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  9. [9] A. Kirsch and S. Ritter, A linear sampling method for inverse scattering from an open arc. Inverse Problems 16 (2000) 89–105. Zbl0968.35129
  10. [10] R. Kreß, Linear integral equations. 2nd edn., Springer, New York (1999). Zbl0920.45001
  11. [11] C. Miranda, Partial differential equations of elliptic type. 2nd edn., Springer, Berlin (1970). Zbl0198.14101MR284700
  12. [12] 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. Zbl0854.65106
  13. [13] 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. Zbl0760.73072
  14. [14] F. Santosa and M. Vogelius, A computational algorithm to determine cracks from electrostatic boundary measurements. Internat. J. Engrg. Sci. 29 (1991) 917–937. Zbl0825.73761

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