Line segment crack recovery from incomplete boundary data

作者: Amel Ben Abda , Moez Kallel , Juliette Leblond , Jean-Paul Marmorat

DOI: 10.1088/0266-5611/18/4/308

关键词: MathematicsMathematical analysisApproximation theoryReciprocity (electromagnetism)Boundary value problemRobin boundary conditionLine segmentMixed boundary conditionNeumann boundary conditionFree boundary problem

摘要: We are concerned with non-destructive control issues, namely detection and recovery of cracks in a planar (2D) isotropic conductor from partial boundary measurements solution to the Laplace–Neumann problem. first build an extension that whole boundary, using constructive approximation techniques classes analytic meromorphic functions, then use localization algorithms based on computations reciprocity gap.

参考文章(22)
I. Chalendar, J. R. Partington, Approximation problems and representations of Hardy spaces in circular domains Studia Mathematica. ,vol. 136, pp. 255- 269 ,(1999)
Walter Rudin, Real and complex analysis ,(1966)
E. DiBenedetto, G. Alessandrini, Determining 2-dimensional cracks in 3-dimensional bodies: Uniqueness and stability Indiana University Mathematics Journal. ,vol. 46, pp. 0- 0 ,(1997) , 10.1512/IUMJ.1997.46.1332
Vadim M Adamjan, Damir Z Arov, Mark Grigorievich Krein, None, ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM Mathematics of The Ussr-sbornik. ,vol. 15, pp. 31- 73 ,(1971) , 10.1070/SM1971V015N01ABEH001531
S. Chaabane, M. Jaoua, J. Leblond, Parameter Identification for Laplace Equation and Approximation in Hardy Classes Journal of Inverse and Ill-posed Problems. ,vol. 11, pp. 33- 57 ,(2003) , 10.1515/156939403322004928
Fadil Santosa, Michael Vogelius, A computational algorithm to determine cracks from electrostatic boundary measurements International Journal of Engineering Science. ,vol. 29, pp. 917- 937 ,(1991) , 10.1016/0020-7225(91)90166-Z
L. Baratchart, J. Leblond, J. R. Partington, Problems of Adamjan—Arov—Krein Type on Subsets of the Circle and Minimal Norm Extensions Constructive Approximation. ,vol. 16, pp. 333- 357 ,(2000) , 10.1007/S003659910015
M. Papadimitrakis, Continuity of the Operator of Best Uniform Approximation by Bounded Analytic Functions Bulletin of the London Mathematical Society. ,vol. 25, pp. 44- 48 ,(1993) , 10.1112/BLMS/25.1.44