The (F*F) ^1/4-method for the transmission problem in two-dimensional linear elasticity

References

• Arens , T . 2001 . Linear sampling methods for 2 d inverse elastic wave scattering . Inverse Problems , 17 : 1445 – 1464 .
   Web of Science ®Google Scholar
• Alves , CJS and Kress , R . 2002 . On the far field operator in elastic obstacle scattering . IMA Journal of Applied Mathematics , 67 : 1 – 21 .
   Web of Science ®Google Scholar
• Charalambopoulos , A , Gindides , D and Kiriaki , K . 2003 . The Linear sampling method for non absorbing penetrable elastic bodies . Inverse Problems , 19 : 549 – 561 .
   Web of Science ®Google Scholar
• Colton , D and Kirsch , A . 1996 . A simple method for solving the inverse scattering problems in the resonance region . Inverse Problems , 12 : 383 – 393 .
   Web of Science ®Google Scholar
• Colton , D , Piana , M and Potthast , R . 1997 . A simple method using Morozov's discrepancy principle for solving inverse scattering problems . Inverse Problems , 13 : 1477 – 1493 .
   Web of Science ®Google Scholar
• Colton , D and Monk , P . 1985 . A novel method for solving the inverse scattering problem for time-harmonic acoustic waves in the resonance region . SIAM Journal on Applied Mathematics , 45 : 1039 – 1053 .
   Web of Science ®Google Scholar
• Colton , D and Piana , M . 1998 . The simple method for solving the electromagnetic inverse scattering problem: the case of TE polarized waves . Inverse Problems , 14 : 597 – 614 .
   Web of Science ®Google Scholar
• Dassios , G and Rigou , Z . 1995 . Elastic Herglotz functions . SIAM Journal on Applied Mathematics , 55 ( 5 ) : 1345 – 1361 .
   Google Scholar
• Dassios , G and Rigou , Z . 1997 . On the reconstruction of a rigid body in the theory of elasticity . Journal of Applied Mathematics and Mechanics , 77 ( 12 ) : 911 – 923 .
   Google Scholar
• Groetsch CW 1984 The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind Boston Pitman
   Google Scholar
• Kirsch A 1996 An Introduction to the Mathematical Theory of Inverse Problems Berlin Springer
   Google Scholar
• Kirsch , A . 1998 . Characterization of the shape of a scattering obstacle using the spectral data of the far field operator . Inverse Problems , 14 : 1489 – 1512 .
   Web of Science ®Google Scholar
• Kirsch , A . 1999 . Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory . Inverse Problems , 15 : 413 – 429 .
   Web of Science ®Google Scholar
• Kirsch A Kress R 1986 An optimization method in inverse acoustic scattering Inverse Problems (Cannon and Hornung, eds). ISNM 77 93 102
   Google Scholar
• Kupradze VD 1965 Potential methods in the theory of elasticity Israel Programm for Scientific Translations Jerusalem
   Google Scholar
• Kupradze VD 1979 Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity North-Holland Amsterdam
   Google Scholar
• Morse PM Feshbach H 1953 Methods of Theoretical Physics Vol. I, II New York McGraw-Hill
   Google Scholar
• Pelekanos , G , Kleinman , RE and Van den Berg , PM . 2000 . A weak form of the conjugate gradient FFT method for two-dimensional elastodynamics . Journal of Computational Physics , 160 : 597 – 611 .
   Google Scholar
• Rynne , BP and Sleeman , BD . 1991 . The interior transmission problem and inverse scattering from inhomogeneous media . SIAM Journal on Applied Mathematics , 22 : 1755 – 1762 .
   Google Scholar
• Sevroglou V Kiriaki K 1999 On Herglotz functions in two dimensional linear elasticity Proceedings of the 4th International Workshop, World Scientific. Scattering Theory and Biomedical Engineering Modelling and Applications pp. 151–158
   Google Scholar
• Sevroglou , V and Pelekanos , G . 2002 . Two dimensional elastic Herglotz functions and their applications in inverse scatteing . Journal of Elasticity , 68 : 123 – 144 .
   Web of Science ®Google Scholar
• Tikhonov AN Goncharsky AV Stepanov VV Yagola AG 1995 Numerical Methods for the Solution of III-Posed Problems Dordrecht Kluwer
   Google Scholar