Free Access
Volume 39, Number 5, September-October 2005
Page(s) 1041 - 1059
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). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  8. A. Bendali, Approximation par éléments Finis de surface de problèmes de diffraction des ondes électromagnétiques. Thèse de Doctorat, Université Paris VI (1984). [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  12. J. Chazarain and A. Piriou, Introduction to the Theory of Linear Partial Differential Equations. North-Holland, Amsterdam/New-York (1982). [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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). [Google Scholar]
  16. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory. Krieger Publishing Company (1992). [Google Scholar]
  17. M. Costabel, Boundary integral operators on Lipschitz domains: elementary results. SIAM J. Math. Anal. 19 (1988) 613. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Costabel and E. Stephan, A direct boundary integral equation method for transmission problems. J. Math. Anal. Appl. 136 (1985) 367. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  20. E. Darve, The fast multipole method. I. Error analysis and asymptotic complexity. SIAM J. Numer. Anal. 38 (2000) 98. [CrossRef] [MathSciNet] [Google Scholar]
  21. E. Darve, The fast multipole method: numerical implementation. J. Comput. Phys. 160 (2000) 195. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  23. D.S. Jones, An improved surface radiation condition. IMA J. Appl. Math. 48 (1992) 163. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  28. J.C. Nédélec, Acoustic and Electromagnetic Equations, Integral Representations for Harmonic Problems. Springer-Verlag, New York. Appl. Math. Sci. 144 (2001). [Google Scholar]
  29. F. Rellich, Über das asymptotische verhalten der lösungen von Δu + λu = 0, in unendlichen gebieten, Jahresber. Deutch. Math. Verein 53 (1943) 57. [Google Scholar]
  30. V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions. J. Comput. Phys. 86 (1990) 414. [CrossRef] [MathSciNet] [Google Scholar]
  31. S.M. Rytov, Calcul du skin-effect par la méthode des perturbations. J. Phys. USSR 2 (1940) 233. [Google Scholar]
  32. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Pub. Co., Boston (1996). [Google Scholar]
  33. T.B.A. Senior, Impedance boundary conditions for imperfectly conducting surface. Appl. Sci. Res. B. 8 (1960) 418. [CrossRef] [MathSciNet] [Google Scholar]
  34. T.B.A. Senior, Approximate boundary conditions for homogeneous dielectric bodies. J. Electromagnet. Wave 9 (1995) 1227. [Google Scholar]
  35. T.B.A. Senior, Generalized boundary conditions for scalar fields. J. Acoust. Soc. Amer. 97 (1995) 3473. [CrossRef] [Google Scholar]
  36. T.B.A. Senior and J.L. Volakis, Approximate Boundary Conditions in Electromagnetics. IEE Electromagnetic Waves, Serie 41, London (1995). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  41. D.S. Wang, Limits and validity of the impedance boundary condition on penetrable surfaces. IEEE. Trans. Antennas Prop. 35 (1987) 453. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you