High frequency approximation of integral equations modeling scattering phenomena

Armel de La Bourdonnaye

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 2, page 223-241
  • ISSN: 0764-583X

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de La Bourdonnaye, Armel. "High frequency approximation of integral equations modeling scattering phenomena." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.2 (1994): 223-241. <http://eudml.org/doc/193737>.

@article{deLaBourdonnaye1994,
author = {de La Bourdonnaye, Armel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {high frequency approximation; scattering problems; incident waves; accuracy; complexity},
language = {eng},
number = {2},
pages = {223-241},
publisher = {Dunod},
title = {High frequency approximation of integral equations modeling scattering phenomena},
url = {http://eudml.org/doc/193737},
volume = {28},
year = {1994},
}

TY - JOUR
AU - de La Bourdonnaye, Armel
TI - High frequency approximation of integral equations modeling scattering phenomena
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 2
SP - 223
EP - 241
LA - eng
KW - high frequency approximation; scattering problems; incident waves; accuracy; complexity
UR - http://eudml.org/doc/193737
ER -

References

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  1. [1] G. BEYLKIN, R. COIFMAN and V. ROKHLIN, 1991, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., XLIV, pp. 141-183. Zbl0722.65022MR1085827
  2. [2] F. X. CANNING, 1992, Sparse approximation for solving integral equations with oscillatory kernels, Siam J. Sci. Stat. Comput., 13. Zbl0749.65093MR1145176
  3. [3] J. CHAZARAIN and A. PIRIOU, 1981, Introduction à la théorie des équations aux dérivées partielles linéaires, Paris, Gauthier-Villars. Zbl0446.35001MR598467
  4. [4] P. COLTON and R. KRESS, 1993, Integral equation method in scattering theory, Pure and Applied Mathematics. Zbl0522.35001
  5. [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. [6] J. J. DUISTERMAAT, 1973, Fourier integral operators, Courant Institute of Mathematical Sciences, New York. Zbl0272.47028MR451313
  7. [7] V. FOCK, 1946, The distribution of currents induced by a plane wave on the surface of a conductor, J. Phys., 10, 130-136. Zbl0063.01396MR17661
  8. [8] V. GUILLEMIN and D. SCHAEFFER, 1973, Remarks on a paper of D. Ludwig, Bull, of the A.M.S. 79. Zbl0256.35008MR410050
  9. [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. Zbl0479.76088MR637242
  10. [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. Zbl0154.12802MR204032
  11. [11] J. NEDELEC, 1980, Mixed finite elements in R3, Numer. Mathematik, 35. Zbl0419.65069
  12. [12] A. F. NIKIFOROV and V. B. UVAROV, 1988, Special fonctions of mathematical physics, Birkhäuser, Basel Boston. Zbl0624.33001MR922041
  13. [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. [14] V. ROKHLIN, 1990, Rapid solution of integral equations of scattering theory in two dimensions, Journal of Computational Physics, 86, 414-439. Zbl0686.65079MR1036660
  15. [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. MR1106007
  16. [16] M. TAYLOR, 1981, Pseudo differential operators, vol. 34 of Princeton mathematical series, Princeton University Press, Princeton. Zbl0453.47026
  17. [17] G. N. WATSON, 1944, A treatise on Bessel functions, Cambridge University Press, 1944. MR10746JFM48.0412.02

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