Free Access
Issue
ESAIM: M2AN
Volume 44, Number 4, July-August 2010
Page(s) 781 - 801
DOI https://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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  5. Y. Boubendir, Techniques de décomposition de domaine et méthode d'équations intégrales. Ph.D. Thesis, INSA, France (2002). [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  15. D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences 93. Springer, Berlin, Germany (1992). [Google Scholar]
  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). [Google Scholar]
  17. M. Darbas, Generalized CFIE for the Iterative Solution of 3-D Maxwell Equations. Appl. Math. Lett. 19 (2006) 834–839. [CrossRef] [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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). [Google Scholar]
  25. P. Monk, Finite Element Methods for Maxwell's Equations, Numerical Mathematics and Scientific Computation. Oxford Science Publication, UK (2003). [Google Scholar]
  26. Multifrontal Massively Parallel Solver, www.enseeiht.fr/lima/apo/MUMPS. [Google Scholar]
  27. J.C. Nédélec, Acoustic and Electromagnic Equations Integral Representation for Harmonic Problems. Springer, New York, USA (2001). [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]

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