High frequency approximation of integral equations modeling scattering phenomena
de La Bourdonnaye, Armel
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994), p. 223-241 / Harvested from Numdam
@article{M2AN_1994__28_2_223_0,
     author = {de La Bourdonnaye, Armel},
     title = {High frequency approximation of integral equations modeling scattering phenomena},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {28},
     year = {1994},
     pages = {223-241},
     mrnumber = {1267199},
     zbl = {0822.65124},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1994__28_2_223_0}
}
de La Bourdonnaye, Armel. High frequency approximation of integral equations modeling scattering phenomena. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 28 (1994) pp. 223-241. http://gdmltest.u-ga.fr/item/M2AN_1994__28_2_223_0/

[1] G. Beylkin, R. Coifman and V. Rokhlin, 1991, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., XLIV, pp. 141-183. | MR 1085827 | Zbl 0722.65022

[2] F. X. Canning, 1992, Sparse approximation for solving integral equations with oscillatory kernels, Siam J. Sci. Stat. Comput., 13. | MR 1145176 | Zbl 0749.65093

[3] J. Chazarain and A. Piriou, 1981, Introduction à la théorie des équations aux dérivées partielles linéaires, Paris, Gauthier-Villars. | MR 598467 | Zbl 0446.35001

[4] P. Colton and R. Kress, 1993, Integral equation method in scattering theory, Pure and Applied Mathematics. | Zbl 0522.35001

[5] A. De La Bourdonnaye, 1991, Accélération du traitement numérique de l'équation de Helmholtz par équations intégrales et parallélisation, thèse de doctorat, Ecole polytechnique, Palaiseau, France.

[6] J. J. Duistermaat, 1973, Fourier integral operators, Courant Institute of Mathematical Sciences, New York. | MR 451313 | Zbl 0272.47028

[7] V. Fock, 1946, The distribution of currents induced by a plane wave on the surface of a conductor, J. Phys., 10, 130-136. | MR 17661 | Zbl 0063.01396

[8] V. Guillemin and D. Schaeffer, 1973, Remarks on a paper of D. Ludwig, Bull, of the A.M.S. 79. | MR 410050 | Zbl 0256.35008

[9] M. Hamdi, 1981, Une formulation variationnelle par équations pour la résolution de l'équation de Helmholtz avec des conditions aux limites mixtes, C. R. Acad. Sc, Série II, t. 292, 17-20. | MR 637242 | Zbl 0479.76088

[10] D. Ludwig, 1967, Uniform asymptotic expansion of the field scattered by a convex object at high frequencies, Comm. Pure Appl. Math., XX, 103-138. | MR 204032 | Zbl 0154.12802

[11] J. Nedelec, 1980, Mixed finite elements in R3, Numer. Mathematik, 35. | Zbl 0419.65069

[12] A. F. Nikiforov and V. B. Uvarov, 1988, Special fonctions of mathematical physics, Birkhäuser, Basel Boston. | MR 922041 | Zbl 0624.33001

[13] S. Rao, D. Wilton and A. Glisson, 1982, Electromagnetic scattering by surface of arbitrary shape, I.E.E.E. Trans. on antennas and propagation, AP-30, 409-418.

[14] V. Rokhlin, 1990, Rapid solution of integral equations of scattering theory in two dimensions, Journal of Computational Physics, 86, 414-439. | MR 1036660 | Zbl 0686.65079

[15] B. Stupfel, R. L. Martret, P. Bonnemason and B. Scheurer, 1991, Combined boundary-element and finite-element method for the scattering problem by axisymmetrical penetrable objects, in Mathematical and numerical aspects of wave propagation phenomena, G. Cohen, L. Halpern and P. Joly, eds., SIAM, 332-341. | MR 1106007

[16] M. Taylor, 1981, Pseudo differential operators, vol. 34 of Princeton mathematical series, Princeton University Press, Princeton. | Zbl 0453.47026

[17] G. N. Watson, 1944, A treatise on Bessel functions, Cambridge University Press, 1944. | JFM 48.0412.02 | MR 10746