Free access
Issue
ESAIM: M2AN
Volume 44, Number 4, July-August 2010
Page(s) 781 - 801
DOI http://dx.doi.org/10.1051/m2an/2010023
Published online 17 March 2010
  1. F. Alouges, S. Borel and D. Levadoux, A stable well conditioned integral equation for electromagnetism scattering. J. Comput. Appl. Math. 204 (2007) 440–451. [CrossRef] [MathSciNet]
  2. X. Antoine and H. Barucq, Microlocal diagonalization of strictly hyperbolic pseudodifferential systems and application to the design of radiation conditions in electromagnetism. SIAM J. Appl. Math. 61 (2001) 1877–1905. [CrossRef] [MathSciNet]
  3. X. Antoine and M. Darbas, Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation. ESAIM: M2AN 41 (2007) 147–167. [CrossRef] [EDP Sciences]
  4. A. Bendali, M'B Fares and J. Gay, A boundary-element solution of the Leontovitch problem. IEEE Trans. Antennas Propagat. 47 (1999) 1597–1605. [CrossRef]
  5. Y. Boubendir, Techniques de décomposition de domaine et méthode d'équations intégrales. Ph.D. Thesis, INSA, France (2002).
  6. A. Buffa, Hodge decomposition on the boundary of a polyhedron: the multi-connected case. Math. Mod. Meth. Appl. Sci. 11 (2001) 1491–1504. [CrossRef] [MathSciNet]
  7. A. Buffa and R. Hiptmair, Galerkin Boundary Element Methods for Electromagnetic Scattering, in Computational Methods in Wave Propagation, M. Ainsworth, P. Davies, D.B. Duncan, P.A. Martin and B. Rynne Eds., Lecture Notes in Computational Science and Engineering 31, Springer-Verlag (2003) 83–124.
  8. F. Cakoni, D. Colton and P. Monk, The electromagnetic inverse scattering problem for partially coated Lipschitz domains. Proc. Royal. Soc. Edinburgh 134A (2004) 661–682. [CrossRef]
  9. 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. Tech. Report CRSC-TR95-13, North Carolina State University, Center for Research in Scientific Computation, USA (1995).
  10. S.L. Campbell, I.C.F. Ipsen, C.T. Kelley and C.D. Meyer, GMRES and the Minimal Polynomial. BIT Numerical Mathematics 36 (1996) 664–675. [CrossRef] [MathSciNet]
  11. H.S. Christiansen, Résolution des équations intégrales pour la diffraction d'ondes acoustiques et électromagnétiques – Stabilisation d'algorithmes itératifs et aspects de l'analyse numérique. Ph.D. Thesis, Centre de Mathématiques Appliquées, UMR 7641, CNRS/École polytechnique, France (2002).
  12. S. 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]
  13. F. Collino, S. Ghanemi and P. Joly, Domain decomposition method for the Helmholtz equation: a general presentation. Comput. Methods Appl. Mech. Eng. 184 (2000) 171–211. [CrossRef]
  14. F. Collino, F. Millot and S. Pernet, Boundary-integral methods for iterative solution of scattering problems with variable impedance surface condition. PIER 80 (2008) 1–28. [CrossRef]
  15. D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences 93. Springer, Berlin, Germany (1992).
  16. M. Darbas, Préconditionneurs analytiques de type Calderon pour les formulations intégrales des problèmes de direction d'ondes. Ph.D. Thesis, INSA Toulouse, France (2004).
  17. M. Darbas, Generalized CFIE for the Iterative Solution of 3-D Maxwell Equations. Appl. Math. Lett. 19 (2006) 834–839. [CrossRef] [MathSciNet]
  18. M. Darbas, Some second-kind integral equations in electromagnetism. Preprint, Cahiers du Ceremade 2006-15 (2006) http://www.ceremade.dauphine.fr/preprints/CMD/2006-15.pdf.
  19. V. Frayssé, L. Giraud, S. Gratton and J. Langou, A Set of GMRES Routines for Real and Complex Arithmetics on High Performance Computers. CERFACS Technical Report, TR/PA/03/3 (2003) http://www.cerfacs.fr/algor/Softs/GMRES/index.html.
  20. J.-F. Lee, R. Lee and R.J. Burkholder, Loop star basis functions and a robust preconditioner for EFIE scattering problems. IEEE Trans. Antennas Propagat. 51 (2003) 1855–1863. [CrossRef]
  21. M.A. Leontovitch, Approximate boundary conditions for the electromagnetic field on the surface of a good conductor, Investigations Radiowave Propagation part II. Academy of Sciences, Moscow, Russia (1978).
  22. J.R. Mautz and R.F. Harrington, A combined-source solution for radiation and scattering from a perfectly conducting body. IEEE Trans. Antennas Propag. AP-27 (1979) 445–454.
  23. 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]
  24. K.M. Mitzner, Numerical solution of the exterior scattering problem at eigenfrequencies of the interior problem. Int. Scientific Radio Union Meeting, Boston, USA (1968).
  25. P. Monk, Finite Element Methods for Maxwell's Equations, Numerical Mathematics and Scientific Computation. Oxford Science Publication, UK (2003).
  26. Multifrontal Massively Parallel Solver, www.enseeiht.fr/lima/apo/MUMPS.
  27. J.C. Nédélec, Acoustic and Electromagnic Equations Integral Representation for Harmonic Problems. Springer, New York, USA (2001).
  28. S.M. Rao, D.R. Wilton and A.W. Glisson, Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antennas Propagat. AP-30 (1982) 409–418.
  29. V. Rokhlin, Diagonal form of translation operators for the Helmholtz equation in three dimensions. Appl. Comput. Harmon. Anal. 1 (1993) 82–93. [CrossRef] [MathSciNet]
  30. 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]
  31. B. Stupfel, A hybrid finite element and integral equation domain decomposition method for the solution of the 3-D scattering problem. J. Comput. Phys. 172 (2001) 451–471. [CrossRef]

Recommended for you