Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T19:02:00.505Z Has data issue: false hasContentIssue false
  • English
  • Français

Crack detection using electrostatic measurements

Published online by Cambridge University Press:  15 April 2002

Martin Brühl ,
Martin Hanke  and
Michael Pidcock
Martin Brühl
Affiliation:
Fachbereich Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany. ([email protected]); ([email protected])
Martin Hanke
Affiliation:
Fachbereich Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany. ([email protected]); ([email protected])
Michael Pidcock
Affiliation:
School of Computing and Mathematical Sciences, Oxford Brookes University, Oxford OX3 0BP, Great Britain. ([email protected])
Get access

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.

Keywords

Inverse boundary value problemnondestructive testingcrack.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 3 , May 2001 , pp. 595 - 605
Copyright
© EDP Sciences, SMAI, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alessandrini, G. and Diaz Valenzuela, A., Unique determination of multiple cracks by two measurements. SIAM J. Control Optim. 34 (1996) 913-921. CrossRef
Brühl, M., Explicit characterization of inclusions in electrical impedance tomography. SIAM J. Math. Anal. 32 (2001) 1327-1341. CrossRef
Brühl, M. and Hanke, M., Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Problems 16 (2000) 1029-1042. CrossRef
Bryan, K. and Vogelius, M., A computational algorithm to determine crack locations from electrostatic boundary measurements. The case of multiple cracks. Internat. J. Engrg. Sci. 32 (1994) 579-603. CrossRef
H. W. Engl, M. Hanke and A. Neubauer, Regularization of inverse problems. Kluwer, Dordrecht (1996).
Friedman, A. and Vogelius, M., Determining cracks by boundary measurements. Indiana Univ. Math. J. 38 (1989) 527-556. CrossRef
Kim, H. and Seo, J. K., Unique determination of a collection of a finite number of cracks from two boundary measurements. SIAM J. Math. Anal. 27 (1996) 1336-1340. CrossRef
Kirsch, A., Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Problems 14 (1998) 1489-1512. CrossRef
Kirsch, A. and Ritter, S., A linear sampling method for inverse scattering from an open arc. Inverse Problems 16 (2000) 89-105. CrossRef
R. Kreß, Linear integral equations. 2nd edn., Springer, New York (1999).
C. Miranda, Partial differential equations of elliptic type. 2nd edn., Springer, Berlin (1970).
Mönch, L., On the numerical solution of the direct scattering problem for an open sound-hard arc. J. Comput. Appl. Math. 71 (1996) 343-356. CrossRef
Nishimura, N. and Kobayashi, S., A boundary integral equation method for an inverse problem related to crack detection. Internat. J. Numer. Methods Engrg. 32 (1991) 1371-1387. CrossRef
Santosa, F. and Vogelius, M., A computational algorithm to determine cracks from electrostatic boundary measurements. Internat. J. Engrg. Sci. 29 (1991) 917-937. CrossRef