M. Abramowitz and . Et-stegun, Handbook of mathematical functions : with formulas, graphs and mathematical tables, 1965.

G. Allaire, Analyse numérique et optimisation, 2002.

S. Andrieux and A. Et-ben-abda, Identification of planar cracks by complete overdetermined data: inversion formulae, Inverse Problems, vol.12, issue.5, pp.553-563, 1996.
DOI : 10.1088/0266-5611/12/5/002

S. Andrieux, B. Abda, A. Bui, and H. , Sur l'identification de fissures planes via le concept d'??cart ?? la r??ciprocit?? en ??lasticit??, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.324, issue.12, pp.1431-1438, 1997.
DOI : 10.1016/S0764-4442(97)83588-4

S. Andrieux, B. Abda, A. Bui, and H. , Reciprocity principle and crack identification, Inverse Problems, vol.15, issue.1, pp.59-65, 1999.
DOI : 10.1088/0266-5611/15/1/010
URL : https://hal.archives-ouvertes.fr/hal-00111614

S. Andrieux, Méthodes et techniques de résolution de quelquesprobì emes inverses, 2003.

E. Bécache and P. Joly, Analyse et approximation de modèles de propagation d'ondes, Analyse numérique Partie2, 2004.

P. ´. Bernhard, Eléments d'optimisation. Cours de la faculté des sciences, 2000.

M. Bonnet, BIE and material differentiation applied to the formulation of obstacle inverse problems. Engineering Analysis with Boundary Elements, pp.121-136, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00092369

M. Bonnet, Equations intégrales etélémentsetéléments defrontì ere, CNRS Edition, 1995.

M. Bonnet, A general boundary-only formula for crack shape sensitivity of integral functionals, C. R. Acad. Sci. Paris, Série II b, vol.327, pp.1215-1221, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00092383

M. Bonnet, Probì emes inverses, 2000.

M. Bonnet and B. B. Et-guzina, Sounding of finite solid bodies by way of topological derivative, International Journal for Numerical Methods in Engineering, vol.55, issue.13, pp.2344-2373, 2004.
DOI : 10.1002/nme.1153
URL : https://hal.archives-ouvertes.fr/hal-00111263

H. Bui, Introduction auxprobì emes inverses en mécanique des matériaux . Direction desétudesdesétudes et recherches d'´ electricité de France, 1993.

H. Bui, A. Constantinescu, and H. Et-maigre, Diffraction acoustique inverse de fissure plane: Solution explicite pour un solide born??, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics-Physics-Astronomy, vol.327, issue.10, pp.971-976, 1999.
DOI : 10.1016/S1287-4620(00)87006-4

H. Bui, A. Constantinescu, and H. Et-maigre, Numerical identification of linear cracks in 2D elastodynamics using the instantaneous reciprocity gap, Inverse Problems, vol.20, issue.4, pp.993-1001, 2004.
DOI : 10.1088/0266-5611/20/4/001

A. Burton and G. Et-miller, The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.323, issue.1553, pp.323-201, 1971.
DOI : 10.1098/rspa.1971.0097

Q. Carayol and F. Et-collino, Error estimates in the fast multipole method for scattering problems Part 1: Truncation of the Jacobi-Anger series, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.2, pp.371-394, 2004.
DOI : 10.1051/m2an:2004017

Q. Carayol and F. Et-collino, Error estimates in the Fast Multipole Method for scattering problems Part 2: Truncation of the Gegenbauer series, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.1, pp.183-221, 2005.
DOI : 10.1051/m2an:2005008

A. Chaigne, Ondes acoustiques, 2001.

W. Chew, J. Jin, C. Lu, E. Michielssen, and J. Song, Fast solution methods in electromagnetics, IEEE Transactions on Antennas and Propagation, vol.45, issue.3, pp.533-543, 1997.
DOI : 10.1109/8.558669

D. Colton, K. Giebermann, and P. Et-monk, A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems, SIAM Journal on Scientific Computing, vol.21, issue.6, pp.2316-2330, 2000.
DOI : 10.1137/S1064827598340159

D. Colton, H. Haddar, and M. Et-piana, The linear sampling method in inverse electromagnetic scattering theory, Inverse Problems, vol.19, issue.6, pp.105-137, 2003.
DOI : 10.1088/0266-5611/19/6/057
URL : https://hal.archives-ouvertes.fr/hal-00744163

D. Colton and A. Et-kirsch, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, vol.12, issue.4, pp.383-393, 1996.
DOI : 10.1088/0266-5611/12/4/003

D. Colton and R. Et-kress, Inverse acoustic and Electromagnetic Scattering theory, 1992.

D. Crighton, A. Dowling, F. Williams, J. Heckl, M. Et-leppington et al., Modern Methods in analytical acoustics, 1992.
DOI : 10.1007/978-1-4471-0399-8

E. Darve, Méthodes multipôles rapides : résolution deséquationsdeséquations de Maxwell par formulation intégrale, Thèse de doctorat, 1999.

E. Darve, The Fast Multipole Method: Numerical Implementation, Journal of Computational Physics, vol.160, issue.1, pp.195-240, 2000.
DOI : 10.1006/jcph.2000.6451

E. Darve, The Fast Multipole Method I: Error Analysis and Asymptotic Complexity, SIAM Journal on Numerical Analysis, vol.38, issue.1, pp.98-128, 2000.
DOI : 10.1137/S0036142999330379

M. A. Epton and B. Et-dembart, Multipole Translation Theory for the Three-Dimensional Laplace and Helmholtz Equations, SIAM Journal on Scientific Computing, vol.16, issue.4, pp.865-897, 1995.
DOI : 10.1137/0916051

K. Erhard, Point source approximation methods in inverse obstacle reconstruction problems, 2005.

K. Erhard and R. Et-potthast, A Numerical Study of the Probe Method, SIAM Journal on Scientific Computing, vol.28, issue.5, 2006.
DOI : 10.1137/040607149

H. A. Eschenauer, V. V. Kobelev, and A. Schumacher, Bubble method for topology and shape optimization of structures, Structural Optimization, vol.24, issue.2, pp.42-51, 1994.
DOI : 10.1007/BF01742933

C. Farhat, R. Tezaur, and R. Et-djellouli, On the solution of three-dimensional inverse obstacle acoustic scattering problems by a regularized Newton method, Inverse Problems, vol.18, issue.5, pp.1229-1246, 2002.
DOI : 10.1088/0266-5611/18/5/302

G. R. Feijoo, A new method in inverse scattering based on the topological derivative, Inverse Problems, vol.20, issue.6, pp.1819-1840, 2004.
DOI : 10.1088/0266-5611/20/6/008

S. Garreau, P. Guillaume, and M. Et-masmoudi, The Topological Asymptotic for PDE Systems: The Elasticity Case, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1756-1778, 2001.
DOI : 10.1137/S0363012900369538

L. Greengard and V. Et-rokhlin, A fast algorithm for particle simulations, Journal of Computational Physics, vol.73, issue.2, pp.325-348, 1987.
DOI : 10.1016/0021-9991(87)90140-9

L. Greengard and V. Et-rokhlin, A new version of the Fast Multipole Method for the Laplace equation in three dimensions, Acta Numerica, vol.448, pp.229-269, 1997.
DOI : 10.1016/0009-2614(92)90053-P

B. Guzina and M. Et-bonnet, Topological derivative for the inverse scattering of elastic waves, The Quarterly Journal of Mechanics and Applied Mathematics, vol.57, issue.2, pp.161-179, 2004.
DOI : 10.1093/qjmam/57.2.161
URL : https://hal.archives-ouvertes.fr/hal-00092401

M. Ikehata, Reconstruction of the shape of the inclusion by boundary measurements, Communications in Partial Differential Equations, vol.23, issue.7-8, pp.1479-1474, 1998.
DOI : 10.2307/2154460

M. Ikehata, Reconstruction of obstacle from boundary measurements, Wave Motion, vol.30, issue.3, pp.205-223, 1999.
DOI : 10.1016/S0165-2125(99)00006-2

V. Isakov, Inverse problems for partial differential equations, 1998.

R. Jakob-chien and B. K. Et-alpert, A Fast Spherical Filter with Uniform Resolution, Journal of Computational Physics, vol.136, issue.2, pp.580-584, 1997.
DOI : 10.1006/jcph.1997.5782

P. Joly, Méthodes mathématiques et numériques enélectromagnétismeenélectromagnétisme, 1996.

P. Joly, Analyse et approximation de modèles de propagation d'ondes, analyse mathématique, 2002.

S. Koc, J. Song, and W. Et-chew, Error Analysis for the Numerical Evaluation of the Diagonal Forms of the Scalar Spherical Addition Theorem, SIAM Journal on Numerical Analysis, vol.36, issue.3, pp.906-921, 1999.
DOI : 10.1137/S0036142997328111

M. Margorani and M. Et-bonnet, Fast multipole method applied to elastostatic BEM-FEM coupling, Computers and Structures, vol.83, pp.700-717, 2005.

M. Masmoudi, A synthetic presentation of shape and topological optimization, Lesprobì emes inverses, le contrôle et l'optimisation de formes, PICOF'98, pp.121-127, 1998.

P. M. Morse and H. Et-feshbach, Methods of Theoretical Physics, American Journal of Physics, vol.22, issue.6, 1953.
DOI : 10.1119/1.1933765

N. Nishimura, Crack determination problems, Theoretical and Appl. Mech, vol.46, pp.39-57, 1997.

N. Nishimura, Fast multipole accelerated boundary integral equation methods, Applied Mechanics Reviews, vol.55, issue.4, pp.299-324, 2002.
DOI : 10.1115/1.1482087

G. Perrin and . Acoustique, Notes de cours de l, 2005.

R. Potthast, A fast new method to solve inverse scattering problems, Inverse Problems, vol.12, issue.5, pp.731-742, 1996.
DOI : 10.1088/0266-5611/12/5/014

R. Potthast, A point source method for inverse acoustic and electromagnetic obstacle scattering problems, IMA Journal of Applied Mathematics, vol.61, issue.2, pp.119-140, 1998.
DOI : 10.1093/imamat/61.2.119

R. Potthast, Point sources and multipoles in inverse scattering theory, 1999.
DOI : 10.1201/9781420035483

R. Potthast, Stability estimates and reconstructions in inverse acoustic scattering using singular sources, Journal of Computational and Applied Mathematics, vol.114, issue.2, pp.247-274, 2000.
DOI : 10.1016/S0377-0427(99)00201-0

R. Potthast, A survey on sampling and probe methods for inverse problems, Inverse Problems, vol.22, issue.2, pp.1-47, 2006.
DOI : 10.1088/0266-5611/22/2/R01

L. Pyl, D. Clouteau, and G. Et-degrande, A weakly singular boundary integral equation in elastodynamics for heterogeneous domains mitaging fictitious eigenfrequencies. Engineering Analysis withe Boundary Elements, pp.1493-1513, 2004.

V. Rokhlin, Rapid solution of integral equations of classical potential theory, Journal of Computational Physics, vol.60, issue.2, pp.187-207, 1985.
DOI : 10.1016/0021-9991(85)90002-6

V. Rokhlin, Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions, Applied and Computational Harmonic Analysis, vol.1, issue.1, pp.82-93, 1993.
DOI : 10.1006/acha.1993.1006

J. Sokolowski and A. Et-zochowski, On the Topological Derivative in Shape Optimization, SIAM Journal on Control and Optimization, vol.37, issue.4, 1997.
DOI : 10.1137/S0363012997323230

J. Sokolowski and A. Et-zochowski, Topological derivatives for elliptic problems, Inverse Problems, vol.15, issue.1, pp.123-134, 1999.
DOI : 10.1088/0266-5611/15/1/016
URL : https://hal.archives-ouvertes.fr/hal-00105955

G. Sylvand, La méthode multipôle rapide enélectromagnétismeenélectromagnétisme : performances, parallélisation, applications, Thèse de doctorat, Ecole Nationale des Ponts et Chaussées, 2002.

A. Tikhonov and V. Et-arsenine, Méthodes de résolution deprobì emes mal posés, Editions Mir, 1976.

K. Yoshida, Applications of Fast Multipole Method to Boundary Integral Equation Method, Thèse de doctorat, 2001.