Free access
Issue
ESAIM: M2AN
Volume 39, Number 5, September-October 2005
Page(s) 1041 - 1059
DOI http://dx.doi.org/10.1051/m2an:2005037
Published online 15 September 2005
  1. X. Antoine, Conditions de Radiation sur le Bord. Ph.D. Thesis, No. d'ordre 395, Université de Pau et des Pays de l'Adour, France (1997).
  2. X. Antoine, Fast approximate computation of a time-harmonic scattered field using the on-surface radiation condition method. IMA J. Appl. Math. 66 (2001) 83. [CrossRef] [MathSciNet]
  3. X. Antoine and H. Barucq, On the construction of approximate boundary conditions for solving the interior problem of the acoustic scattering transmission problem, in Domain Decomposition Methods in Science and Engineering. R. Kornhuber, R. Hoppe, J. Periaux, O. Pironneau, O. Widlund, J. Xu, Eds., Springer Series. Lect. Notes Comput. Sci. Engrg. 40 (2004) 133–140. [CrossRef]
  4. X. Antoine, H. Barucq and L. Vernhet, Approximate solution for the scattering of a time-harmonic wave by a homogeneous dissipative obstacle. Internal Report MIP 00-20, Laboratoire MIP, Toulouse (2000).
  5. X. Antoine, H. Barucq and L. Vernhet, High-frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions. Asymptot. Anal. 26 (2001) 257. [MathSciNet]
  6. X. Antoine, A. Bendali and M. Darbas, Analytic preconditioners for the electric field integral equation. Internat. J. Numer. Methods Engrg. 61 (2004) 1310–1331. [CrossRef] [MathSciNet]
  7. X. Antoine, A. Bendali and M. Darbas, Analytic preconditioners for the boundary integral solution of the scattering of acoustic waves by open surfaces. J. Comput. Acoustics, Special Issue on High Performance Scientific Computing in Acoustics 13 (2005). To appear.
  8. A. Bendali, Approximation par éléments Finis de surface de problèmes de diffraction des ondes électromagnétiques. Thèse de Doctorat, Université Paris VI (1984).
  9. A. Bendali and M. Souilah, Consistency estimates for a double-layer potential and application to the numerical analysis of the boundary-element approximation of acoustic scattering by a penetrable object. Math. Comp. 62 (1994) 65. [CrossRef] [MathSciNet]
  10. B. Carpinteri, I.S. Duff and L. Giraud, Experiments with sparse preconditioning of dense problems of electromagnetic applications. Technical Report TR/PA/00/04, CERFACS, France (2000).
  11. B. Carpinteri, I.S. Duff and L. Giraud, Sparse pattern selection strategies for robust Frobenius norm minimization preconditioners in electromagnetism. Numer. Linear Algebra Appl. 7 (2000) 667. [CrossRef] [MathSciNet]
  12. J. Chazarain and A. Piriou, Introduction to the Theory of Linear Partial Differential Equations. North-Holland, Amsterdam/New-York (1982).
  13. K. Chen and P.J. Harris, Efficient preconditioners for iterative solution of the boundary element equations for the three-dimensional Helmholtz equation. Appl. Numer. Math. 36 (2001) 475. [CrossRef] [MathSciNet]
  14. S.H. Christiansen and J.C. Nédélec, Des préconditionneurs pour la résolution numérique des équations intégrales de frontière de l'acoustique. C. R. Acad. Sci. Paris Sér. I Math. 330 (2000) 617.
  15. P.G. Ciarlet, Handbook of Numerical Analysis, Vol. II, Finite Element Methods (Part I). P.G. Ciarlet and J.-L. Lions, Eds., Elsevier Science Publisher, North-Holland, Amsterdam (1991).
  16. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory. Krieger Publishing Company (1992).
  17. M. Costabel, Boundary integral operators on Lipschitz domains: elementary results. SIAM J. Math. Anal. 19 (1988) 613. [CrossRef] [MathSciNet]
  18. M. Costabel and E. Stephan, A direct boundary integral equation method for transmission problems. J. Math. Anal. Appl. 136 (1985) 367. [CrossRef] [MathSciNet]
  19. E. Darrigrand, Coupling of fast multipole method and microlocal discretization for the 3-D Helmholtz equation. J. Comput. Phys. 181 (2002) 126. [CrossRef] [MathSciNet]
  20. E. Darve, The fast multipole method. I. Error analysis and asymptotic complexity. SIAM J. Numer. Anal. 38 (2000) 98. [CrossRef] [MathSciNet]
  21. E. Darve, The fast multipole method: numerical implementation. J. Comput. Phys. 160 (2000) 195. [CrossRef] [MathSciNet]
  22. R. Djellouli, C. Farhat, A. Macedo and R. Tezaur, Three-dimensional finite element calculations in acoustic solution scattering using arbitrarily convex artificial boundaries. Internat. J. Numer. Methods Engrg. 53 (2002) 1461. [CrossRef]
  23. D.S. Jones, An improved surface radiation condition. IMA J. Appl. Math. 48 (1992) 163. [CrossRef] [MathSciNet]
  24. R.E. Kleinman and P.A. Martin, On single integral equations for the transmission problem of acoustics. SIAM J. Appl. Math. 48 (1988) 307. [CrossRef] [MathSciNet]
  25. G.A. Kriegsmann, A. Taflove and K.R. Umashankar, A new formulation of electromagnetic wave scattering using the on-surface radiation condition approach. IEEE Trans. Antennas Prop. 35 (1987) 153. [CrossRef]
  26. D. Levadoux, Étude d'une équation intégrale adaptée à la résolution haute-fréquence de l'équation d'Helmholtz. Thèse de Doctorat, Université Paris VI (2001).
  27. D. Levadoux and B. Michielsen, Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes. ESAIM: M2AN 38 (2004) 157–175. [CrossRef] [EDP Sciences]
  28. J.C. Nédélec, Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems. Springer-Verlag, New York. Appl. Math. Sci. 144 (2001).
  29. F. Rellich, Über das asymptotische verhalten der lösungen von Δu + λu = 0, in unendlichen gebieten, Jahresber. Deutch. Math. Verein 53 (1943) 57.
  30. V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions. J. Comput. Phys. 86 (1990) 414. [CrossRef] [MathSciNet]
  31. S.M. Rytov, Calcul du skin-effect par la méthode des perturbations. J. Phys. USSR 2 (1940) 233.
  32. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Pub. Co., Boston (1996).
  33. T.B.A. Senior, Impedance boundary conditions for imperfectly conducting surface. Appl. Sci. Res. B. 8 (1960) 418. [CrossRef] [MathSciNet]
  34. T.B.A. Senior, Approximate boundary conditions for homogeneous dielectric bodies. J. Electromagnet. Wave 9 (1995) 1227.
  35. T.B.A. Senior, Generalized boundary conditions for scalar fields. J. Acoust. Soc. Amer. 97 (1995) 3473. [CrossRef]
  36. T.B.A. Senior and J.L. Volakis, Approximate Boundary Conditions in Electromagnetics. IEE Electromagnetic Waves, Serie 41, London (1995).
  37. T.B.A. Senior, J.L. Volakis and S.R. Legault, Higher order impedance and absorbing boundary conditions. IEEE Trans. Antennas Prop. 45 (1997) 107. [CrossRef]
  38. O. Steinbach and W.L. Wendland, The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9 (1998) 191. [CrossRef] [MathSciNet]
  39. L. Vernhet, Approximation par éléments finis de frontière de problèmes de diffraction d'ondes avec condition d'impédance. Ph.D. Thesis, Université de Pau et des Pays de l'Adour, No. 400, France (1997).
  40. L. Vernhet, Boundary element solution of a scattering problem involving a generalized impedance boundary condition. Math. Methods Appl. Sci. 22 (1999) 587. [CrossRef] [MathSciNet]
  41. D.S. Wang, Limits and validity of the impedance boundary condition on penetrable surfaces. IEEE. Trans. Antennas Prop. 35 (1987) 453. [CrossRef]

Recommended for you