Generalized topological derivative for the Navier equation and inverse scattering in the time domain

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 49-50, 2008, Pages 4467-4484

  Chikichev, Ivan ^a,b   Guzina, Bojan B ^a,b  

^a EXXONMOBIL UPSTREAM RESEARCH COMPANY   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Elastic waves; Imaging; Inverse scattering; Material identification; Penetrable defects; Topological sensitivity; Transmission problem

Indexed keywords

ASYMPTOTIC ANALYSIS; COMPUTER SIMULATION; DEFECTS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; ELASTIC WAVES; EPITAXIAL GROWTH; GREEN'S FUNCTION; IMAGE RECONSTRUCTION; REPAIR; RESTORATION; SCATTERING; THREE DIMENSIONAL; TIME DOMAIN ANALYSIS; TOPOLOGY;

3-D RECONSTRUCTIONS; ADJOINT; BOUNDARY INTEGRALS; COST FUNCTIONAL; DEFECT RECONSTRUCTION; DEFECT-FREE; DIRECT APPROACH; ELASTIC SOLIDS; FIRST ORDERS; FREQUENCY DOMAINS; IMAGING; INVERSE SCATTERING; MATERIAL CHARACTERIZATIONS; MATERIAL IDENTIFICATION; NEGATIVE VALUES; NON-INVASIVE; NUMERICAL SIMULATIONS; PENETRABLE DEFECTS; REFERENCE DOMAINS; SAMPLING POINTS; TIME DOMAIN OCT; TIME HARMONICS; TOPOLOGICAL DERIVATIVES; TOPOLOGICAL SENSITIVITY; TRANSIENT ELASTIC WAVES; TRANSIENT SCATTERED FIELDS; TRANSMISSION PROBLEM; WAVEFIELDS; WAVEFORMS;

SENSITIVITY ANALYSIS;

EID: 52749087179     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.05.019     Document Type: Article

References (51)

1. Achenbach J.D. Wave Propagation in Elastic Solids (1984), North-Holland, Amsterdam
2. Aki K., and Richards P.G. Quantitative Seismology (2002), University Science Books, Sausalito, CA
3. Ammari H., and Kang H. Reconstruction of the Small Inhomogeneities from Boundary Measurements (2004), Springer, Berlin, New York
4. Ammari H., Kang H., Nakamura G., and Tanuma K. Complete asymptotic expansion of the solutions of the system of the elastostatics in the presence of an inclusion of the small diameter and detection of the inclusion. J. Elasticity 67 2 (2002) 97-129
5. Arens T. Linear sampling methods for 2D inverse elastic wave scattering. Inverse Problems 17 (2001) 1445-1464
6. Baganas K., Guzina B.B., Charalambopoulos A., and Manolis G.D. A linear sampling method for the inverse transmission problem in near-field elastodynamics. Inverse Problems 22 (2006) 1835-1853
7. Ben-Menahem A., and Singh S.J. Seismic Waves and Sources (1981), Springer Verlag, New York
8. Blomgren P., Papanicolaou G., and Zhao H. Super-resolution in time-reversal acoustics. J. Acoustic Soc. Am. 111 (2002) 230-248
9. Bonnet M. BIE and material differentiation applied to the formulation of obstacle inverse problems. Engrg. Anal. Bound. Elem. 15 (1995) 121-136
10. Bonnet M. Boundary Integral Equation Methods for Solids and Fluids (1999), John Wiley & Sons
11. Bonnet M. Topological sensitivity for 3D elastodynamics and acoustic inverse scattering in the time domain. Comp. Methods Appl. Mech. Engrg. 195 (2006) 5239-5254
12. Bonnet M., and Guzina B.B. Sounding of finite bodies by way of topological derivative. Int. J. Numer. Methods Engrg. 61 (2004) 2344-2373
13. Bracewell R. The Filtering or Interpolating Function, sinc(x) in the Fourier Transform and its Applications (1999), McGraw-Hill
14. Cakoni F., and Colton D. Qualitative Methods in Inverse Scattering Theory (2006), Springer-Verlag, Berlin
15. Charalambopoulos A., Gintides D., and Kiriaki K. The linear sampling method for the transmission problem in three-dimensional linear elasticity. Inverse Problems 18 (2002) 547-558
16. Cheney M., Isaacson D., and Newell J.C. Electrical impedance tomography. SIAM Rev. 41 1 (1999) 85-101
17. Colton D., Coyle J., and Monk P. Recent developments in inverse acoustic scattering theory. SIAM Rev. 42 (2000) 369-414
18. Colton D., and Kirsch A. A simple method for solving inverse scattering problems in the resonance region. Inverse Problems 12 (1996) 383-393
19. Colton D., and Monk P. Linear sampling method for the detection of leukemia using microwaves. SIAM J. Appl. Math. 58 (1998) 926-941
20. Dahlquist G., and Bjorck A. Numerical Methods (1974), Prentice-Hall, Englewood Cliffs, NJ
21. Devaney A.J. Time reversal imaging of obscured targets from multistatic data. IEEE Trans. Antennas Prop. 53 5 (2005) 1600-16105
22. Dominguez N., Gibiat V., and Esquerre Y. Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection. Wave Motion 42 (2005) 31-52
23. Doyley M.M., Van Houten E.E., Weaver J.B., Poplack S., Duncan L., Kennedy K.D., and Paulsen F. Shear modulus estimation using parallelized partial reconstruction. IEEE Trans. Med. Imag. 23 (2004) 1404-1416
24. Eschenauer H.A., Kobelev V.V., and Schumacher A. Bubble method for topology and shape optimization of structures. Struct. Optim. 8 (1994) 42-51
25. Fatemi M., and Greenleaf J.F. Probing the dynamics of tissue at low frequencies with the radiation force of ultrasound. Phys. Med. Biol. 45 (2000) 1449-1464
26. Feijoo G.R. A new method in inverse scattering based on the topological derivative. Inverse Problems 20 (2004) 1819-1840
27. Gallego R., and Rus G. Identification of cracks and cavities using the topological sensitivity boundary integral equation. Comp. Mech. 33 (2004) 154-163
28. Garreau S., Guillaume P., and Masmoudi M. The topological asymptotic for PDE systems: the elasticity case. SIAM J. Control Optim. 39 (2001) 1756-1778
29. Guzina B.B., and Bonnet M. Topological derivative for the inverse scattering of elastic waves. Quart. J. Mech. Appl. Math. 57 (2004) 161-179
30. Guzina B.B., and Bonnet M. Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics. Inverse Problems 22 (2006) 1761-1785
31. Guzina B.B., and Chikichev I. From imaging to material identification: a generalized concept of topological sensitivity. J. Mech. Phys. Solids 55 (2007) 245-275
32. Guzina B.B., and Madyarov A. A linear sampling approach to inverse elastic scattering in piecewise-homogeneous domains. Inverse Problems 23 (2007) 1467-1493
33. Guzina B.B., and Pak R.Y.S. On the analysis of wave motions in a multi-layered solid. Quart. J. Mech. Appl. Math. 54 1 (2001) 13-37
34. Kennett B.L.N. Seismic Wave Propagation in Stratified Media. Advances in Applied Mechanics vol. 21 (1981), Academic Press
35. Madyarov A.I., and Guzina B.B. A radiation condition for layered elastic media. J. Elasticity 82 (2006) 73-98
36. Masmoudi M., Pommier J., and Samet B. The topological asymptotic expansion for the maxwell equations and some applications. Inverse Problems 21 (2005) 547-564
37. Mueller J.L., and Siltanen S. Direct reconstructions of conductivities from boundary measurements. SIAM J. Sci. Comp. 24 4 (2003) 1232-1266
38. Mura T. Micromechanics of Defects in Solids (1987), Martinus Nijhoff Publishers, Dordreght, Boston, Lancaster
39. Nintcheu Fata S., and Guzina B.B. Elastic scatterer reconstruction via the adjoint sampling method. SIAM J. Appl. Math 67 (2007) 1330-1352
40. Nintcheu Fata S., and Guzina B.B. A linear sampling method for near-field inverse problems in elastodynamics. Inverse Problems 20 (2004) 713-736
41. Committee on Fracture Characterization and Fluid Flow National Research Council. Rock Fractures and Fluid Flow: Contemporary Understanding and Applications. National Academies Press, 1996.
42. Pak R.Y.S., and Guzina B.B. Seismic soil-structure interaction analysis by direct boundary element methods. Int. J. Solids Struct. 36 (1999) 4743-4766
43. Porat B. A Course in Digital Signal Processing (1996), John Wiley and Sons
44. Potthast R. Point Sources and Multipoles in Inverse Scattering Theory (2001), Chapman and Hal/CRC, New York
45. Potthast R. A survey on sampling and probe methods for inverse problems. Inverse Problems 22 (2006) R1-R47
46. Schroeder C.T., Scott W.R., and Larson G.D. Elastic waves interacting with buried land mines: a study using the FDTD method. IEEE Trans. Geosci. Remote Sens. 40 (2002) 1405-1415
47. A. Schumacher, Topologieoptimierung von bauteilstrukturen unter verwendung von kopchpositionierungkrieterien, Ph.D. Thesis, University of Siegen, Germany, 1995.
48. Sheriff R.E., and Geldart L.P. Exploration Seismology (1995), Cambridge University Press, Cambridge, UK
49. Sokolowski J., and Zochowski A. On the topological derivative in shape optimization. SIAM J. Control Optim. 37 (1999) 1251-1272
50. Sokolowski J., and Zolesio J.P. Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer Series in Computational Mathematics vol. 16 (1992), Springer-Verlag
51. Vogelius M.S., Cedio-Fengya D.J., and Moskow S. Identification of conductivity imperfections of small diameter by boundary measurements. continuous dependence and computational reconstruction. Inverse Problems 14 (1998) 553-595