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.
Mots-clés : inverse boundary value problem, nondestructive testing, crack
@article{M2AN_2001__35_3_595_0,
author = {Br\"uhl, Martin and Hanke, Martin and Pidcock, Michael},
title = {Crack detection using electrostatic measurements},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {595--605},
publisher = {EDP-Sciences},
volume = {35},
number = {3},
year = {2001},
mrnumber = {1837086},
zbl = {0985.35103},
language = {en},
url = {http://www.numdam.org/item/M2AN_2001__35_3_595_0/}
}
TY - JOUR AU - Brühl, Martin AU - Hanke, Martin AU - Pidcock, Michael TI - Crack detection using electrostatic measurements JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 595 EP - 605 VL - 35 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_2001__35_3_595_0/ LA - en ID - M2AN_2001__35_3_595_0 ER -
%0 Journal Article %A Brühl, Martin %A Hanke, Martin %A Pidcock, Michael %T Crack detection using electrostatic measurements %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 595-605 %V 35 %N 3 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_2001__35_3_595_0/ %G en %F M2AN_2001__35_3_595_0
Brühl, Martin; Hanke, Martin; Pidcock, Michael. Crack detection using electrostatic measurements. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 3, pp. 595-605. http://www.numdam.org/item/M2AN_2001__35_3_595_0/
[1] and, Unique determination of multiple cracks by two measurements. SIAM J. Control Optim. 34 (1996) 913-921. | Zbl
[2] , Explicit characterization of inclusions in electrical impedance tomography. SIAM J. Math. Anal. 32 (2001) 1327-1341. | Zbl
[3] and, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Problems 16 (2000) 1029-1042. | Zbl
[4] and, A computational algorithm to determine crack locations from electrostatic boundary measurements. The case of multiple cracks. Internat. J. Engrg. Sci. 32 (1994) 579-603. | Zbl
[5] , and, Regularization of inverse problems. Kluwer, Dordrecht (1996). | MR | Zbl
[6] and, Determining cracks by boundary measurements. Indiana Univ. Math. J. 38 (1989) 527-556. | Zbl
[7] and, Unique determination of a collection of a finite number of cracks from two boundary measurements. SIAM J. Math. Anal. 27 (1996) 1336-1340. | Zbl
[8] , Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Problems 14 (1998) 1489-1512. | Zbl
[9] and, A linear sampling method for inverse scattering from an open arc. Inverse Problems 16 (2000) 89-105. | Zbl
[10] , Linear integral equations. 2nd edn., Springer, New York (1999).
[11] , Partial differential equations of elliptic type. 2nd edn., Springer, Berlin (1970). | MR | Zbl
[12] , On the numerical solution of the direct scattering problem for an open sound-hard arc. J. Comput. Appl. Math. 71 (1996) 343-356. | Zbl
[13] and, A boundary integral equation method for an inverse problem related to crack detection. Internat. J. Numer. Methods Engrg. 32 (1991) 1371-1387. | Zbl
[14] and, A computational algorithm to determine cracks from electrostatic boundary measurements. Internat. J. Engrg. Sci. 29 (1991) 917-937. | Zbl
