Free Access
Issue
ESAIM: M2AN
Volume 50, Number 1, January-February 2016
Page(s) 263 - 288
DOI https://doi.org/10.1051/m2an/2015042
Published online 28 January 2016
  1. C. Ahrens and G. Beylkin, Rotationally invariant quadratures for the sphere. Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 465 (2009) 3103–3125. [NASA ADS] [CrossRef] [Google Scholar]
  2. C. Amrouche, V. Girault and J. Giroire, Weighted Sobolev spaces for Laplace’s equation in Rn. J. Math. Pures Appl. 73 (1994) 579–606. [Google Scholar]
  3. N. Arar and T.Z. Boulmezaoud, Eigenfunctions of a weighted Laplace operator in the whole space. J. Math. Anal. Appl. 400 (2013) 161–173. [CrossRef] [Google Scholar]
  4. K. Atkinson and W. Han, Spherical harmonics and approximations on the unit sphere: An introduction. Vol. 2044 of Lect. Notes Math. Springer, Heidelberg (2012). [Google Scholar]
  5. A. Bayliss and E. Turkel, Radiation boundary conditions for wavelike equations. Commun. Pure Appl. Math. 33 (1980) 707–725. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.-P. Bérenger, A perfectly matched layer for absorption of electromagnetics waves. J. Comput. Phys. 114 (1994) 185–200. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  7. J.-P. Bérenger. Perfectly matched layer for the fdtd solution of wave-structure interaction problems. IEEE Trans. Antennas Propag. 44 (1996) 110–117,. [CrossRef] [Google Scholar]
  8. Ch. Bernardi and Y. Maday, Approximations spectrales de problèmes aux limites elliptiques, Vol. 10 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer–Verlag, Paris (1992). [Google Scholar]
  9. P. Bettess, Infinite elements. Int. J. Numer. Methods Engrg. 11 (1977) 53–64. [CrossRef] [Google Scholar]
  10. P. Bettess and O. C. Zienkiewicz. Diffraction and refraction of surface waves using finite and infinite elements. Int. J. Numer. Methods Engrg. 11 (1977) 1271–1290. [CrossRef] [MathSciNet] [Google Scholar]
  11. T.Z. Boulmezaoud. On the Laplace operator and on the vector potential problems in the half-space: an approach using weighted spaces. Math. Methods Appl. Sci. 26 (2003) 633–669. [CrossRef] [MathSciNet] [Google Scholar]
  12. T.Z. Boulmezaoud, On the invariance of weighted Sobolev spaces under Fourier transform. C. R. Math. Acad. Sci. Paris 339 (2004) 861–866. [CrossRef] [MathSciNet] [Google Scholar]
  13. T.Z. Boulmezaoud, Inverted finite elements: a new method for solving elliptic problems in unbounded domains. ESAIM: M2AN 39 (2005) 109–145. [CrossRef] [EDP Sciences] [Google Scholar]
  14. T.Z. Boulmezaoud and K. Kaliche, A new numerical method for the model of solvation in continuum anisotropic dielectrics. In preparation (2015). [Google Scholar]
  15. T.Z. Boulmezaoud and U. Razafison, On the steady Oseen problem in the whole space. Hiroshima Math. J. 35 (2005) 371–401. [MathSciNet] [Google Scholar]
  16. T.Z. Boulmezaoud, S. Mziou and T. Boudjedaa, Numerical approximation of second-order elliptic problems in unbounded domains. J. Sci. Comput. 60 (2014) 295–312. [CrossRef] [Google Scholar]
  17. J.P. Boyd, Orthogonal rational functions on a semi-infinite interval. J. Comput. Phys. 70 (1987) 63–88. [CrossRef] [Google Scholar]
  18. J.P. Boyd, Spectral methods using rational basis functions on an infinite interval. J. Comput. Phys. 69 (1987) 112–142. [CrossRef] [Google Scholar]
  19. C.A. Brebbia, J.C.F. Telles and L.C. Wrobel, Boundary Element Techniques. Springer-Verlag, Berlin (1984). [Google Scholar]
  20. F. Brezzi, C. Johnson and J.-C. Nédélec, On the Coupling of Boundary Integral and Finite Element Methods. In Proc. of the Fourth Symposium on Basic Problems of Numerical Mathematics Plzevn. Charles Univ., Prague (1978) 103–114. [Google Scholar]
  21. D.S. Burnett, A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion. J. Acoust. Soc. Amer. 96 (1994) 2798–2816. [CrossRef] [MathSciNet] [Google Scholar]
  22. C. Canuto, S. I. Hariharan and L. Lustman, Spectral methods for exterior elliptic problems. Numer. Math. 46 (1985) 505–520. [CrossRef] [MathSciNet] [Google Scholar]
  23. C. Carstensen, D. Zarrabi and E.P. Stephan, On the h-adaptive coupling of FE and BE for viscoplastic and elastoplastic interface problems. J. Comput. Appl. Math. 75 (1996) 345–363. [CrossRef] [Google Scholar]
  24. J. Céa, Approximation variationnelle des problèmes aux limites. Ann. Inst. Fourier Grenoble 14 (1964) 345–444. [CrossRef] [MathSciNet] [Google Scholar]
  25. Ph.-G. Ciarlet, The finite element method for elliptic problems. North-Holland Publishing Co., Amsterdam (1978). [Google Scholar]
  26. D.L. Colton and R. Kressn, Integral equation methods in scattering theory. Pure Appl. Math. John Wiley & Sons Inc., New York (1983). [Google Scholar]
  27. R. Cools, Constructing cubature formulae: the science behind the art. In vol. 6 of Acta Numer. Cambridge Univ. Press, Cambridge (1997) 1–54. [Google Scholar]
  28. M. Costabel and E.P. Stephan, Coupling of finite and boundary element methods for an elastoplastic interface problem. SIAM J. Numer. Anal. 27 (1990) 1212–1226. [CrossRef] [MathSciNet] [Google Scholar]
  29. M. Costabel, V.J. Ervin and E.P. Stephan, Symmetric coupling of finite elements and boundary elements for a parabolic-elliptic interface problem. Quart. Appl. Math. 48 (1990) 265–279. [MathSciNet] [Google Scholar]
  30. B. Enquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31 (1977) 629–651. [CrossRef] [MathSciNet] [Google Scholar]
  31. B. Enquist and A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations. Commun. Pure Appl. Math. 32 (1979) 313–357. [CrossRef] [Google Scholar]
  32. D. Funaro, Computational aspects of pseudospectral Laguerre approximations. Appl. Numer. Math. 6 (1990) 447–457. [CrossRef] [Google Scholar]
  33. D. Funaro and O. Kavian, Approximations of some diffusion evolution equations in unbounded domains by Hermite functions. Math. Comput. 57 (1990) 597–619. [CrossRef] [Google Scholar]
  34. K. Gerdes and L. Demkowicz, Solution of 3D-Laplace and Helmholtz equations in exterior domains using hp-infinite elements. Comput. Methods Appl. Mech. Engrg. 137 (1996) 239–273. [CrossRef] [MathSciNet] [Google Scholar]
  35. J. Giroire, Études de quelques problèmes aux limites extérieurs et résolution par équations intégrales. Ph.D. thesis, Université Pierre et Marie Curie, Paris (1987). [Google Scholar]
  36. J. Giroire and J.-C. Nédélec, Numerical solution of an exterior Neumann problem using a double layer potential. Math. Comput. 32 (1978) 973–990. [CrossRef] [MathSciNet] [Google Scholar]
  37. B.-Y. Guo, J. Shen and Z.-Q. Wang, A rational approximation and its applications to differential equations on the half line. J. Sci. Comput. 15 (2000) 117–147. [CrossRef] [Google Scholar]
  38. B. Hanouzet, Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace. Rend. Sem. Mat. Univ. Padova 46 (1971) 227–272. [MathSciNet] [Google Scholar]
  39. W.J. Hehre, L. Radom, P.V.R. Schleyer and J.A. Pople, Ab initio molecular orbital theory. Wiley (1986). [Google Scholar]
  40. C. Johnson and J.-C. Nédélec, On the coupling of boundary integral and finite element methods. Math. Comput. 35 (1980) 1063–1079. [CrossRef] [MathSciNet] [Google Scholar]
  41. Q.T. Le Gia and H.N. Mhaskar, Localized linear polynomial operators and quadrature formulas on the sphere. SIAM J. Numer. Anal. 47 (2008/09) 440–466. [Google Scholar]
  42. J. Lysmer and R.L. Kuhlemeyer, Finite difference model for infinite media. J. Eng. Mech. EMR 95 (1969) 859–877. [Google Scholar]
  43. Y. Maday, B. Pernaud-Thomas and H. Vandeven, Reappraisal of Laguerre type spectral methods. La Recherche Aerospatiale 6 (1985) 13–35. [Google Scholar]
  44. A.D. McLaren, Optimal numerical integration on a sphere. Math. Comput. 17 (1963) 361–383. [CrossRef] [Google Scholar]
  45. C. Müller, Spherical harmonics. Vol. 17 of Lect. Notes Math. Springer-Verlag, Berlin (1966). [Google Scholar]
  46. C. Müller, Analysis of Spherical Symmetries in Euclidean Spaces. Vol. 129 of Applied Mathematical Sciences. Springer (1998). [Google Scholar]
  47. A. Ralston and Ph. Rabinowitz, A first course in numerical analysis, 2nd edition. Dover Publications, Inc., Mineola, New York (2001). [Google Scholar]
  48. R.T. Seeley, Spherical harmonics. Amer. Math. Monthly 73 (1966) 115–121. [CrossRef] [MathSciNet] [Google Scholar]

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