Free access
Issue
ESAIM: M2AN
Volume 41, Number 1, January-February 2007
Page(s) 147 - 167
DOI http://dx.doi.org/10.1051/m2an:2007009
Published online 26 April 2007
  1. F. Alouges, S. Borel and D. Levadoux, A new well-conditionned integral formulation for Maxwell Equations in three dimensions. IEEE Trans. Ant. Prop. 53 (2005) 2995–3004. [CrossRef]
  2. S. Amini and S.M. Kirkup, Solution of Helmholtz equation in exterior domain by elementary boundary integral equations. J. Comput. Phys. 118 (1995) 208–221. [CrossRef] [MathSciNet]
  3. S. Amini and N.D. Maines, Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation. Internat. J. Numer. Methods Engrg. 41 (1998) 875–898. [CrossRef] [MathSciNet]
  4. X. Antoine, Fast approximate computation of a time-harmonic scattered field using the On-Surface Radiation Condition method. IMA J. Appl. Math. 66 (2001) 83–110. [CrossRef] [MathSciNet]
  5. X. Antoine, Some Applications of the On-Surface Radiation Condition to the Integral Equations for Solving Electromagnetic Scattering Problems. Industrial Mathematics and Statistics, Narosa Publishing (2003).
  6. X. Antoine and M. Darbas, Alternative integral equations for the iterative solution of acoustic scattering problems. Quaterly J. Mech. Appl. Math. 58 (2005) 107–128. [CrossRef]
  7. X. Antoine, H. Barucq and A. Bendali, Bayliss-Turkel-like radiation condition on surfaces of arbitrary shape. J. Math. Anal. Appl. 229 (1999) 184–211. [CrossRef] [MathSciNet]
  8. 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]
  9. X. Antoine, M.Darbas and Y.Y. Lu, An improved surface radiation condition for high-frequency acoustics scattering problems. Comput. Meth. Appl. Mech. Eng. 195 (2006) 4060–4074. [CrossRef]
  10. J.J. Bowman, T.B.A. Senior and P.L.E. Uslenghi, Electromagnetic and acoustic scattering by simple shapes. North-Holland Publishing Compagny, Amsterdam (1969).
  11. A. Brakhage and P. Werner, Über das Dirichletsche Aussenraumproblem für die Helmholtzsche Schwingungsgleichung. Arch. Math. 16 (1965) 325–329. [CrossRef] [MathSciNet]
  12. O.P. Bruno and L.A. Kunyansky, A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests, and applications. J. Comput. Phys. 169 (2001) 80–110. [CrossRef] [MathSciNet]
  13. O.P. Bruno and L.A. Kunyansky, Surface scattering in three dimensions: an accelerated high-order solver. P. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001) 2921–2934. [CrossRef]
  14. A. Buffa and R. Hiptmair, A coercive combined field integral equation for electromagnetic scattering. SIAM J. Numer. Anal. 42 (2004) 621–640. [CrossRef] [MathSciNet]
  15. A. Buffa and R. Hiptmair, Regularized combined field integral equations. Numer. Math. 100 (2005) 1–19. [CrossRef] [MathSciNet]
  16. D.C. Calvo, M.D. Collins and D.K. Dacol, A higher-order on-surface radiation condition derived from an analytic representation of a Dirichlet-to-Neumann map. IEEE. Trans. Antennas Progat. 51 (2003) 1607–1614. [CrossRef]
  17. S.L. Campbell, I.C.F. Ipsen, C.T. Kelley, C.D. Meyer and Z.Q. Xue, Convergence estimates for solution of integral equations with GMRES. J. Integral Equations Appl. 8 (1996) 19–34. [CrossRef] [MathSciNet]
  18. B. Carpintieri, I.S. Duff and L. Giraud, Experiments with sparse approximate preconditioning of dense linear problems from electromagnetic applications. Technical Report TR/PA/00/04, Cerfacs, France (2000).
  19. B. Carpintieri, I.S. Duff and L. Giraud, Sparse pattern selection strategies for robust Froebenius norm minimization preconditioners in electromagnetism, Preconditioning Techniques for Large Sparse Matrix Problems in Industrial Applications (Minneapolis, MN, 1999). Numer. Lin. Alg. Appl. 7 (2000) 667–685. [CrossRef] [MathSciNet]
  20. G. Chen and J. Zhou, Boundary Element Methods. Academic Press, Harcourt Brace Jovanovitch, Publishers (1992).
  21. K. Chen, On a class of preconditioning methods for dense linear systems from boundary elements. SIAM J. Sci. Comput. 20 (1998) 684–698. [CrossRef] [MathSciNet]
  22. K. Chen, Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems. Electron. Trans. Numer. Anal. 8 (1999) 138–153. [MathSciNet]
  23. K. Chen, An analysis of sparse approximate inverse preconditioners for boundary elements. SIAM J. Matrix Anal. Appl. 22 (2001) 1958–1978.
  24. 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) 475–489. [CrossRef] [MathSciNet]
  25. W.C. Chew and Warnick, On the spectrum of the electric field integral equation and the convergence of the moment method. Internat. J. Numer. Methods Engrg. 51 (2001) 31–56. [CrossRef] [MathSciNet]
  26. W.C. Chew, J-M. Jin, E. Michielssen and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics. Artech House Antennas and Propagation Library, Norwood (2001).
  27. 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 330 (2000) 617–622.
  28. S.H. Christiansen and J.C. Nédélec, A preconditioner for the electric field integral equation based on Calderon formulas. SIAM J. Numer. Anal. 40 (2002) 1100–1135. [CrossRef] [MathSciNet]
  29. D. Colton and R. Kress, Integral Equations in Scattering Theory. Pure and Applied Mathematics, John Wiley and Sons, New York (1983).
  30. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory. Second Edition, Applied Mathematical Sciences 93, Springer-Verlag, Berlin (1998).
  31. M. Darbas, Préconditionneurs Analytiques de type Calderòn pour les Formulations Intégrales des Problèmes de Diffraction d'ondes. Ph.D. Thesis, Université P. Sabatier, Toulouse, France (November 2004).
  32. M. Darbas, Generalized CFIE for the iterative solution of 3-D Maxwell Equations. Appl. Math. Lett. 19 (2006) 834–839. [CrossRef] [MathSciNet]
  33. J.M. Ford, An improved discrete wavelet transform preconditioner for dense matrix problems. SIAM J. Matrix Anal. Appl. 25 (2003) 642–661. [CrossRef] [MathSciNet]
  34. R.F. Harrington and J.R. Mautz, H-field, E-field and combined field solution for conducting bodies of revolution. Arch. Elektron. Übertragungstech (AEÜ) 32 (1978) 157–164.
  35. P.L. Ho and Y.Y. Lu, Improving the beam propagation method for TM polarization. Opt. Quant. Electron. 35 (2003) 507–519. [CrossRef]
  36. D.S. Jones, Surface radiation conditions. IMA J. Appl. Math. 41 (1988) 21–30. [CrossRef] [MathSciNet]
  37. D.S. Jones, An approximate boundary condition in acoustics. J. Sound Vibr. 121 (1988) 37–45. [CrossRef]
  38. D.S. Jones, An improved surface radiation condition. IMA J. Appl. Math. 48 (1992) 163–193. [CrossRef] [MathSciNet]
  39. C.T. Kelley and Z.Q. Xue, GMRES and integral operators. SIAM J. Sci. Comput. 17 (1996) 217–226. [CrossRef] [MathSciNet]
  40. R. Kress, Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering. Quaterly J. Mech. Appl. Math. 38 (1985) 323–341. [CrossRef]
  41. G.A. Kriegsmann, A. Taflove and K.R. Umashankar, A new formulation of electromagnetic wave scattering using the on-surface radiation condition method. IEEE Trans. Antennas Propag. 35 (1987) 153–161. [CrossRef]
  42. D.P. Levadoux and B.L. Michielsen, Analysis of a boundary integral equation for high frequency Helmholtz equation, 4th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, 1–5 June (1998) 765–767.
  43. D.L. Levadoux and B.L. Michielsen, New integral equation formulations for wave scattering problems. ESAIM: M2AN 38 (2004) 157–176. [CrossRef] [EDP Sciences]
  44. Y.Y. Lu and P.L. Ho, Beam propagation method using a [(p - 1)/p] Padé approximant of the propagator. Opt. Lett. 27 (2002) 683–685. [CrossRef] [PubMed]
  45. W. Mc Lean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge, UK (2000).
  46. F.A. Milinazzo, C.A. Zala, G.H. Brooke, Rational square-root approximations for parabolic equation algorithms. J. Acoust. Soc. Am. 101 (1997) 760–766 [CrossRef]
  47. I. Moret, A note on the superlinear convergence of GMRES. SIAM J. Numer. Anal. 34 (1997) 513–516. [CrossRef] [MathSciNet]
  48. V. Rokhlin, Rapid solution of integral equations of scattering theory in two dimensions. J. Comput. Phys. 86 (1990) 414–439. [CrossRef] [MathSciNet]
  49. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Pub. Co., Boston (1996).
  50. Y. Saad and M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7 (1986) 856–869. [CrossRef] [MathSciNet]
  51. O. Steinbach and W.L. Wendland, The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9 (1998) 191–216. [CrossRef] [MathSciNet]
  52. D. Yevick, A guide to electric-field propagation techniques for guided-wave optics. Opt. Quant. Electron. 26 (1994) 185–197. [CrossRef]

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