T. Abboud, J. Nédélec, and B. Zhou, Méthodes deséquationsdeséquations intégrales pour les hautes fréquences, C. R. Acad. Sci, pp.165-170, 1994.

T. Abboud, J. Nédélec, and B. Zhou, Improvement of the Integral Equation Method for High Frequency Problems, Third international conference on mathematical aspects of wave propagation phenomena, SIAM, pp.178-187, 1995.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1972.

B. Alpert, G. Beylkin, R. Coifman, and V. Rokhlin, Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations, SIAM Journal on Scientific Computing, vol.14, issue.1, pp.159-184, 1993.
DOI : 10.1137/0914010

G. Arfken, Mathematical Methods for Physicists, 1985.

V. M. Babi? and V. S. Buldyrev, Short-Wavelength Diffraction Theory, 1991.
DOI : 10.1007/978-3-642-83459-2

N. Bartoli, Modèles pour la diffraction d'ondes par des obstacles revêtus de couches minces -Résolution deprobì emes de diffraction d'ondes via une formulation intégrale de type point selle, Thèse de doctorat, 2000.

N. Bartoli and F. Collino, Integral Equations via Saddle Point Problem for Acoustic Problems, pp.1023-1049, 2000.

A. Bendali, Approximation parélémentsparéléments finis de surface deprobì emes de diffraction des ondesélectromagnétiquesondesélectromagnétiques, Thèse de doctorat, 1984.

A. N. Bespalov, Cost-effective solution of the boundary integral equations for 3D Maxwell problems, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.14, issue.5, pp.403-428, 1999.
DOI : 10.1515/rnam.1999.14.5.403

G. Beylkin, R. Coifman, and V. Rokhlin, Fast Wavelet Transforms and Numerical Algorithms, Comm. Pure Appl. Math, vol.XLIV, pp.141-183, 1991.

D. Bouche and F. Molinet, Méthodes asymptotiques enélectromagnétismeenélectromagnétisme, 1994.

M. Brandfass and W. C. Chew, A Multilevel Fast Multipole Based Approach for Efficient Reconstruction of Perfectly Conducting Scatterers, Journal of Electromagnetic Waves and Applications, vol.13, issue.1, pp.81-106, 2001.
DOI : 10.1163/156939301X00670

F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, 1991.
DOI : 10.1007/978-1-4612-3172-1

O. P. Bruno and L. A. Kunyansky, A Fast, High-Order Algorithm for the Solution of Surface Scattering Problems: Basic Implementation, Tests, and Applications, Journal of Computational Physics, vol.169, issue.1, pp.80-110, 2001.
DOI : 10.1006/jcph.2001.6714

O. P. Bruno and L. A. Kunyansky, Surface scattering in three dimensions: an accelerated high-order solver, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.457, issue.2016, pp.2921-2934, 2001.
DOI : 10.1098/rspa.2001.0882

F. X. Canning, The Impedance Matrix Localisation (IML) Method for the Moment- Method Calculations. IEEE Antennas and Propagation Magazine, pp.18-30, 1990.

F. X. Canning, Sparse Approximation for Solving Integral Equations with Oscillatory Kernels, SIAM Journal on Scientific and Statistical Computing, vol.13, issue.1, pp.71-87, 1992.
DOI : 10.1137/0913004

J. Chazarain and A. Piriou, IntroductionàIntroduction`Introductionà la théorie deséquationsdeséquations aux dérivées partielles linéaires, 1981.

H. Cheng, L. Greengard, and V. Rokhlin, A Fast Adaptive Multipole Algorithm in Three Dimensions, Journal of Computational Physics, vol.155, issue.2, pp.468-498, 1999.
DOI : 10.1006/jcph.1999.6355

G. Cohen and P. Joly, Aspects récents en méthodes numériques pour leséquationsleséquations de Maxwell, 1998.

R. Coifman, V. Rokhlin, and S. Wandzura, The fast multipole method for the wave equation: a pedestrian prescription, IEEE Antennas and Propagation Magazine, vol.35, issue.3, pp.7-12, 1993.
DOI : 10.1109/74.250128

F. Collino and B. Després, Integral equations via saddle point problems for time-harmonic Maxwell's equations, Journal of Computational and Applied Mathematics, vol.150, issue.1, 2000.
DOI : 10.1016/S0377-0427(02)00658-1

F. Collino and K. Mer-nkonga, The Fast Multipole Method Applied to a Mixed Integral System for Time-Harmonic Maxwell's Equations, JEE 02 : European Symposium on Numerical Methods in Electromagnetics, pp.121-126, 2002.

F. Collino and F. Millot, Méthodes multipôles pour leséquationsleséquations intégrales de Després, CERFACS, 2000.

F. Collino and F. Millot, A 2-Components Algorithm for the Multilevel Fast Multipole Method for Solving Large Scale Diffraction Problems, JEE 02 : European Symposium on Numerical Methods in Electromagnetics, pp.103-108, 2002.

D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theorie, 1992.

E. Darrigrand, Coupling of Fast Multipole Method and Microlocal Discretization for the 3-D Helmholtz Equation, Journal of Computational Physics, vol.181, issue.1, pp.126-154, 2002.
DOI : 10.1006/jcph.2002.7091

URL : https://hal.archives-ouvertes.fr/hal-00133688

E. Darve, Fast-multipole method: a mathematical study, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.325, issue.9, pp.1037-1042, 1997.
DOI : 10.1016/S0764-4442(97)89101-X

E. Darve, Méthodes multipôles rapides : Résolution deséquationsdeséquations de Maxwell par formulations intégrales, Thèse de doctorat, 1999.

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

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, Efficient Fast Multipole Method for Low Frequency Scattering. submitted to, J. Comput. Phys, 2001.

I. Daubechies, Ten Lectures on Wavelets, CBMS Lecture Notes, SIAM, vol.61, 1992.

A. De and L. Bourdonnaye, Convergence de l'approximation par des fonctions oscillantes d'une onde dans la limite des hautes fréquences, C. R. Acad. Sci, pp.765-768, 1994.

A. De and L. Bourdonnaye, High Frequency Approximation of Integral Equations Modelizing Scattering Phenomena, Mod. Math. et Anal. Num, vol.28, issue.2, pp.223-241, 1994.

A. De and L. Bourdonnaye, Une méthode de discrétisation microlocale et son applicationà application`applicationà unprobì eme de diffraction, C. R. Acad. Sci, pp.385-388, 1994.

A. De, L. Bourdonnaye, and M. Tolentino, Discrétisation d'un opérateur pseudodifférentiel d'ordre 1 en hautes fréquences, C. R. Acad. Sci. Paris, vol.320, pp.507-510, 1995.

B. Després, Fonctionnelle quadratique etéquationsetéquations intégrales pour lesprobì emes d'onde harmonique en domaine extérieur, pp.31679-732, 1997.

B. Després, Fonctionnelle quadratique etéquationsetéquations intégrales, Aspects récents en méthodes numériques pour leséquationsleséquations de Maxwell, pp.2-81, 1998.

K. C. Donepudi, J. Jin, S. Velamparambil, J. Song, and W. C. Chew, A higher order parallelized multilevel fast multipole algorithm for 3-D scattering, IEEE Transactions on Antennas and Propagation, vol.49, issue.7, pp.1069-1078, 2001.
DOI : 10.1109/8.933487

A. Dutt, M. Gu, and V. Rokhlin, Fast Algorithms for Polynomial Interpolation, Integration, and Differentiation, SIAM Journal on Numerical Analysis, vol.33, issue.5, pp.1689-1711, 1996.
DOI : 10.1137/0733082

M. A. Epton and B. 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

A. A. Ergin, B. Shanker, and E. Michielssen, The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena, IEEE Antennas and Propagation Magazine, vol.41, issue.4, pp.39-52, 1999.
DOI : 10.1109/74.789736

J. Giroire, Etude de quelquesprobì emes aux limites extérieurs et résolution paréquationsparéquations intégrales, Thèse de doctorat, 1987.

W. L. Golik, Wavelet packets for fast solution of electromagnetic integral equations, IEEE Transactions on Antennas and Propagation, vol.46, issue.5, pp.618-624, 1998.
DOI : 10.1109/8.668902

W. L. Golik, Sparsity and conditioning of impedance matrices obtained with semi-orthogonal and bi-orthogonal wavelet bases, IEEE Transactions on Antennas and Propagation, vol.48, issue.4, pp.473-481, 2000.
DOI : 10.1109/8.843660

L. Greengard and V. Rokhlin, The rapid evaluation of potential fields in three dimensions, In Vortex Methods in Lecture Notes in Mathematics, vol.37, pp.121-141, 1988.
DOI : 10.1007/BFb0089775

L. Greengard and V. 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

T. and H. Duong, Equations intégrales pour la résolution numérique deprobì emes de diffraction d'ondes acoustiques dans

L. Hörmander, The Analysis of Linear Partial Differential Operators I, 1983.

B. Hu, W. C. Chew, E. Michielssen, and J. Zhao, Fast Inhomogeneous Plane-Wave Algorithm (FIPWA) for the Fast Analysis of Two-Dimensional Scattering Problems, 1999.

D. Jiao, M. Lu, E. Michielssen, and J. Jin, A fast time-domain finite element-boundary integral method for electromagnetic analysis, IEEE Transactions on Antennas and Propagation, vol.49, issue.10, pp.491453-1461, 2001.
DOI : 10.1109/8.954934

S. Koc, J. M. Song, and W. C. 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

V. Lange, Equations intégrales espace-temps pour leséquationsleséquations de Maxwell. Calcul du champ diffracté par un obstacle dissipatif, Thèse de doctorat, 1995.

V. Lecompte, CompatibilitéCompatibilitéélectromagnétique d'un téléphone portable avec son environnement, Thèse de doctorat, 1997.

M. Lemou, Fast Multipole Method for Multidimensional Integrals, C. R. Acad. Sci, pp.105-110, 1998.

C. Lu and W. C. Chew, A Multilevel Algorithm for Solving a Boundary Integral Equation of Wave Scattering. Microwave Opt, pp.466-470, 1994.

V. Lubet, Diffraction d'une ondé electromagnétique sur un corps 3.D. Résolution par méthode intégrale avecélémentsavecéléments plans et triangulaires, 1991.

P. A. Martin, Multiple scattering and the Rehr-Albers-Fritzsche formula for the propagator matrix, Journal of Physics A: Mathematical and General, vol.31, issue.44, pp.8923-8932, 1998.
DOI : 10.1088/0305-4470/31/44/016

R. B. Melrose and M. E. Taylor, Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle, Advances in Mathematics, vol.55, issue.3, pp.242-315, 1985.
DOI : 10.1016/0001-8708(85)90093-3

K. Mer-nkonga-rapport and C. Do, Reformulation deséquationsdeséquations intégrales de Després, validations et optimisation du code Maxiim, 1999.

K. Mer-nkonga, The Fast Multipole Method Applied to a Mixed Integral System for Time-Harmonic Maxwell's Equations, Second International Conference on Boundary Integral Methods : Theory and Applications, 2000.

K. Nabors, F. T. Korsmeyer, F. T. Leighton, and J. White, Preconditioned, Adaptive, Multipole-Accelerated Iterative Methods for Three-Dimensional First-Kind Integral Equations of Potential Theory, SIAM Journal on Scientific Computing, vol.15, issue.3, pp.714-735, 1994.
DOI : 10.1137/0915046

J. Nédélec, Résolution deséquationsdeséquations d'ondes acoustiques etélectromagnétiquesetélectromagnétiques, 1999.

J. Nédélec, Acoustic and Electromagnetic Equations, Integral Representation for Harmonic Problems, 2001.

J. Rahola, Diagonal forms of the translation operators in the fast multipole algorithm for scattering problems, BIT Numerical Mathematics, vol.11, issue.3, pp.333-358, 1996.
DOI : 10.1007/BF01731987

P. A. Raviart and J. M. Thomas, IntroductionàIntroduction`Introductionà l'analyse numérique deséquationsdeséquations aux dérivées partielles, 1983.

M. Reed and B. Simon, Scattering theory, 1979.
DOI : 10.1007/BFb0079274

V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions, Journal of Computational Physics, vol.86, issue.2, pp.414-439, 1990.
DOI : 10.1016/0021-9991(90)90107-C

V. Rokhlin, Diagonal Forms of Translation Operators for the Helmholtz Equation in Three Dimensions, Applied and Computational Harmonic Analysis, vol.1, issue.1, 1992.
DOI : 10.1006/acha.1993.1006

S. A. Sauter, Variable Order Panel Clustering, Computing, vol.64, issue.3, pp.223-261, 2000.
DOI : 10.1007/s006070050045

H. Schwichtenberg, G. Winter, and H. Wallmeier, Acceleration of molecular mechanic simulation by parallelization and fast multipole techniques, Parallel Computing, vol.25, issue.5, pp.535-546, 1999.
DOI : 10.1016/S0167-8191(99)00014-9

J. M. Song and W. C. Chew, Multilevel Fast Multipole Algorithm for Solving Combined Field Integral Equations of Electromagnetic Scattering. Microwave Opt, pp.14-19, 1995.

J. M. Song, C. Lu, and W. C. Chew, Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects, IEEE Transactions on Antennas and Propagation, vol.45, issue.10, pp.1488-1493, 1997.
DOI : 10.1109/8.633855

E. M. Stein, Harmonic Analysis : Real Variable Methods, Orthogonality and Oscillatory Integrals, 1993.

B. Stupfel, A Hybrid Finite Element and Integral Equation Domain Decomposition Method for the Solution of the 3-D Scattering Problem, Journal of Computational Physics, vol.172, issue.2, pp.451-471, 2001.
DOI : 10.1006/jcph.2001.6814

G. Sylvand, La méthode multipôle rapide enélectromagnétismeenélectromagnétisme : Performances, parallélisation , applications, Thèse de doctorat, 2002.

J. Tausch, Wavelet and Multipole Sparsification to Integral Equations on Geometrically Complicated Boundaries, Second International Conference on Boundary Integral Methods : Theory and Applications, 2000.

M. E. Taylor, Pseudodifferential Operators, 1981.
DOI : 10.1007/978-1-4419-7052-7_1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.232.4597

M. Tolentino, Résolution hautes fréquences d'´ equations intégrales par une méthode de discrétisation microlocale, Thèse de doctorat, Ecole Nationale des Ponts et Chaussées, 1997.

L. Vernhet, Approximation parélémentsparéléments finis defrontì ere desprobì emes de diffraction d'ondes avec condition d'impédance, Thèse de doctorat, 1997.

R. L. Wagner and W. C. Chew, A Ray-Propagation Fast Multipole Algorithm. Microwave Opt, pp.435-438, 1994.

R. L. Wagner and W. C. Chew, A study of wavelets for the solution of electromagnetic integral equations, IEEE Transactions on Antennas and Propagation, vol.43, issue.8, pp.802-810, 1995.
DOI : 10.1109/8.402199

Y. Xu, Calculation of the Addition Coefficients in Electromagnetic Multisphere-Scattering Theory, Journal of Computational Physics, vol.127, issue.2, pp.285-298, 1996.
DOI : 10.1006/jcph.1996.0175

Y. Xu, Calculation of the Addition Coefficients in Electromagnetic Multisphere-Scattering Theory, Journal of Computational Physics, vol.134, issue.1, p.200, 1997.
DOI : 10.1006/jcph.1997.5687

N. Yarvin and V. Rokhlin, A Generalized One-Dimensional Fast Multipole Method with Application to Filtering of Spherical Harmonics, Journal of Computational Physics, vol.147, issue.2, pp.594-609, 1998.
DOI : 10.1006/jcph.1998.6104

N. Yarvin and V. Rokhlin, An Improved Fast Multipole Algorithm for Potential Fields on the Line, SIAM Journal on Numerical Analysis, vol.36, issue.2, pp.629-666, 1999.
DOI : 10.1137/S0036142997329232

B. Zhou, Méthode deséquationsdeséquations intégrales pour la résolution desprobì emes de diffractionà diffraction`diffractionà hautes fréquences, Thèse de doctorat, 1995.