Fast non-iterative methods for defect identification

European Journal of Computational Mechanics

Volumn 17, Issue 5-7, 2008, Pages 571-582

  Bonnet, Marc ^a   Guzina, Bojan B ^c   Nemitz, Nicolas ^a,b  

^a LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Fast multipole method; Inverse problems; Topological sensitivity

Indexed keywords

BOUNDARY ELEMENT METHOD; DEFECTS; ITERATIVE METHODS; NUMERICAL METHODS; TOPOLOGY;

DEFECT CAVITY; DEFECT IDENTIFICATION; DEFECT INDICATOR; DIRECT SOLUTION; FAST COMPUTATION; FAST-MULTIPOLE METHODS; NON-ITERATIVE METHOD; NUMERICAL SOLUTION METHOD; TOPOLOGICAL SENSITIVITY; UNKNOWN GEOMETRY;

INVERSE PROBLEMS;

EID: 84900816697     PISSN: 26422085     EISSN: 26422050     Source Type: Journal    
DOI: 10.3166/REMN.17.571-582     Document Type: Article

References (43)

1. Ammari H., Kang H., Reconstruction of small inhomogeneities from boundary measurements, Lecture Notes in Mathematics 1846, Springer-Verlag, 2004.
2. Bonnet M., "BIE and material differentiation applied to the formulation of obstacle inverse problems.", Engng. Anal. with Bound. Elem., vol. 15, p. 121-136, 1995.
3. Bonnet M., Boundary Integral Equations Methods for Solids and Fluids, John Wiley and Sons, 1999a.
4. Bonnet M., "Boundary element based formulations for crack shape sensitivity analysis", Engng. Anal. with Bound. Elem., vol. 25, p. 347-362, 2001.
5. Bonnet M., "Topological sensitivity for 3D elastodynamic and acoustic inverse scattering in the time domain", Comp. Meth. in Appl. Mech. Engng., vol. 195, p. 5239-5254, 2006.
6. Bonnet M., "Inverse acoustic scattering by small-obstacle expansion of misfit function", 2007, under review.
7. Bonnet M., Burczyński T., Nowakowski M., "Sensitivity analysis for shape perturbation of cavity or internal crack using BIE and adjoint variable approach", Int. J. Solids Struct., vol. 39, p. 2365-2385, 2002.
8. Bonnet M., Constantinescu A., "Inverse problems in elasticity", Inverse Problems, vol. 21, p. R1-R50, 2005. topical review article.
9. Bonnet M., Guzina B. B., "Sounding of finite solid bodies by way of topological derivative", Int. J. Num. Meth. in Eng., vol. 61, p. 2344-2373, 2004.
10. Bonnet M., Reynier M., "On the estimation of the geometrical support of modelling defects using the distributed error in constitutive equation.", Inverse Problems, Control and Shape Optimization, Carthage, Tunisie, p. 65-70, 1998.
11. Bui H. D., Fracture mechanics. Inverse problems and solutions, Springer-Verlag, 2006.
12. Chaillat S., Bonnet M., Semblat J. F., "A fast multipole accelerated BEM for 3-D elastic wave computation", Revue Européenne de Mécanique Numérique, vol. 17, p. 701-712, 2008.
13. Colton D., Coyle J., Monk P., "Recent developments in inverse acoustic scattering theory.", SIAM Review, vol. 42, p. 369-414, 2000.
14. Colton D., Kirsch A., "A simple method for solving inverse scattering problems in the resonance region", Inverse Problems, vol. 12, p. 383-393, 1996.
15. Darve E., "The fast multipole method: numerical implementation" , J. Comp. Phys., vol. 160, p. 195-240, 2000.
16. Eschenauer H. A., Kobelev V. V., Schumacher A., "Bubble method for topology and shape optimization of structures", Structural Optimization, vol. 8, p. 42-51, 1994.
17. Farhat C., Tezaur R., Djellouli R., "On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method", Inverse Problems, vol. 18, p. 1229-1246, 2002.
18. Feijóo G. R., "A new method in inverse scattering based on the topological derivative", Inverse Problems, vol. 20, p. 1819-1840, 2004.
19. Gallego R., Rus G., "Identification of cracks and cavities using the topological sensitivity boundsary integral equation", Comp. Mech., vol. 33, p. 154-163, 2004.
20. Garreau S., Guillaume P., Masmoudi M., "The topological asymptotic for PDE systems: the elasticity case.", SIAM J. Contr. Opt., vol. 39, p. 1756-1778, 2001.
21. Greengard L., Rokhlin V., "A new version of the fast multipole method for the Laplace equation in three dimensions", Acta Numerica, vol. 6, p. 229-270, 1997.
22. Guzina B. B., Bonnet M., "Topological derivative for the inverse scattering of elastic waves", Quart. J. Mech. Appl. Math., vol. 57, p. 161-179, 2004.
23. Guzina B. B., Bonnet M., "Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics", IP, vol. 22, p. 1761-1785, 2006.
24. Guzina B. B., Chikichev I., "From imaging to material identification: a generalized concept of topological sensitivity", J. Mech. Phys. Solids, vol. 55, p. 245-279, 2007.
25. Guzina B. B., Nintcheu Fata S., Bonnet M., "On the stress-wave imaging of cavities in a semiinfinite solid", Int. J. Solids Struct., vol. 40, p. 1505-1523, 2003.
26. Ladevèze P., Chouaki A., "Application of a posteriori error estimation for structural model updating", Inverse Problems, vol. 15, p. 49-58, 1999.
27. Ladeveze P., Reynier M., Nedjar D., "Parametric correction of finite element models using modal tests.", in H. D. B. M. Tanaka (ed.), Inverse problems in engineering mechanics, Springer-Verlag, p. 91-100, 1993.
28. Lambert M., Bonnet M., Lesselier D., "Introduction à la diffraction inverse en acoustique et élasticité", in M. Bruneau, C. Potel (eds), Matériaux et acoustique, Hermes, p. 82-101, 2006.
29. Litman A., Lesselier D., Santosa F., "Reconstruction of a two-dimensional binary obstacle by controlled evolution of a level-set", Inverse Problems, vol. 14, p. 685-706, 1998.
30. Margonari M., Bonnet M., "Fast multipole method applied to the coupling of elastostatic BEM with FEM", Computers and Structures, vol. 83, p. 700-717, 2005.
31. Masmoudi M., Pommier J., Samet B., "The topological asymptotic expansion for the Maxwell equations and some applications", Inverse Problems, vol. 21, p. 547-564, 2005.
32. Michalewicz Z., Fogel D. B., How to solve it: modern heuristics, Springer-Verlag, 2004.
33. Nemitz N., Méthode multipôle rapide et sensibilité topologique pour l'identification approchée de défauts à partir de données de type acoustique, thèse de doctorat, Ecole Polytechnique, Palaiseau, France, 2006.
34. Nemitz N., Bonnet M., "Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering", Engng. Anal. with Bound. Elem., 2007. (accepté).
35. Nintcheu Fata S., Guzina B. B., "A linear sampling method for near-field inverse problems in elastodynamics", Inverse Problems, vol. 20, p. 713-736, 2004.
36. Nishimura N., "Fast multipole accelerated boundary integral equation methods", Appl. Mech. Rev., vol. 55, p. 299-324, 2002.
37. Pommier J., Samet B., "The topological asymptotic for the Helmholtz equation with Dirichlet condition on the boundary of an arbitrarily shaped hole", SIAM J. Control Optim., vol. 43, p. 899-921, 2005.
38. Potthast R., "A survey on sampling and probe methods for inverse problems", Inverse Problems, vol. 22, p. R1-R47, 2006.
39. Samet B., Amstutz S., Masmoudi M., "The topological asymptotic for the Helmholtz equation", SIAM J. Control Optim., vol. 42, p. 1523-1544, 2004.
40. Schumacher A., Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lochpositionierungskriterien, thèse de doctorat, Univ. of Siegen, Germany, 1995.
41. Sokolowski J., Zochowski A., "On the topological derivative in shape optimization.", SIAM J. Control Optim., vol. 37, p. 1251-1272, 1999.
42. Sylvand G., "Complex industrial computations in electromagnetism using the fast multipole method", in G. Cohen, E. Heikkola, P. Joly, P. Neittaanmäki (eds), Mathematical and numerical methods aspects of wave propagation, Springer-Verlag, p. 657-662, 2003.
43. Tarantola A., Inverse problem theory and methods for model parameter estimation, SIAM, 2005.