Boundary-integral methods for iterative solution of scattering problems with variable impedance surface condition

Progress in Electromagnetics Research

Volumn 80, Issue , 2008, Pages 1-28

  Collino, F ^a   Millot, F ^a   Pernet, S ^a  

^a CERFACS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY ELEMENT METHOD; ELECTROMAGNETISM; INTEGRAL EQUATIONS; PROBLEM SOLVING;

BOUNDARY INTEGRAL METHODS; IMPEDANCE SURFACE CONDITION;

SCATTERING;

EID: 40449140294     PISSN: 10704698     EISSN: 15598985     Source Type: Journal    
DOI: 10.2528/PIER07103105     Document Type: Article

References (30)

1. Leontovitch, M. A., "Approximate boundary conditions for the electromagnetic field on the surface of a good conductor," Investigations Radiowave Propagation Part II, Academy of Sciences, Moscow, 1978.
2. Monk, P., "Finite element methods for Maxwell's equations," Numerical Mathematics and Scientific Computation, Oxford Science Publication, 2003.
3. Stupfel, B., "A hybrid finite element and integral equation domain decomposition method for the solution of the 3-D scattering problem," Journal of Computational Physics, Vol. 172, No. 2, 451-471, September 20, 2001.
4. Collino, F., S. Ghanemi, and P. Joly, "Domain decomposition method for the Helmholtz equation: A general presentation," Comput. Methods Appl. Mech. Eng., Vol. 184, Nos. 2-4, 171-211, 2000.
5. Boubendir, Y., "Techniques de décomposition de domaine et méthode d'équations intégrales," Ph.D. thesis, INSA, Juin 2002.
6. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. AP-30, 409-418, May 1982.
7. Bendali, A., M.'B. Fares, and J. Gay, "A boundary-element solution of the Leontovitch problem," IEEE Transaction on Antennas and Propagation, Vol. 47, No. 10, 1597-1605, 1999.
8. Ammari, H., C. Latiri-Grouz, and J. C. Nédélec, "Scattering of Maxwell's equations with a Leontovitch boundary condition in an inhomogeneous medium: A singular perturbation problem," SIAM J. of Appl. Math., Vol. 59, 1322-1334, 1999.
9. Lange, V., "Equations intégrales espace-temps pour les équations de Maxwell. Calcul du champ diffracté par un obstacle dissipatif," Ph.D. thesis, Université de Bordeaux I, Oct. 1995.
10. Colton, D. and R. Kress, "Inverse acoustic and electromagnetic scattering theory," Applied Mathematical Sciences, Vol. 93, Springer, Berlin, 1992.
11. Rumsey, V. H., "Reaction concept in electromagnetic theory," Physical Review, Vol. 94, 1483-1491, 1954.
12. Makhlouf, A., "Résolution de problèmes de diffraction d'ondes électromagnétiques par équations intégrales de frontière avec condition d'impédance," CERFACS Working Note WN/EMC/04/93, 2004, available online: http://www.cerfacs.fr/emc/.
13. Nédélec, J. C., Acoustic and Electromagnetic Equations Integral Representation for Harmonic Problems, Springer, New-York, 2001.
14. Frayssé, V., 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, available online: http://www.cerfacs.fr/algor/reports/algo_reports_2003.html.
15. Christiansen, S. H. and J.-C. Nédélec, "A preconditioner for the electric field integral equation based on Calderon formulas," SIAM Journal on Numerical Analysis, SINUM Vol. 40, Issue 3, 1100-1135, 2002.
16. Buffa, A. and S. H. Christiansen, "A dual finite element complex on the barycentric refinement," Comptes Rendus Mathématique, Vol. 340, Issue 6, 461-464, 2005.
17. Carpentieri, B., I. S. Duff, and L. Giraud, "A class of spectral two-level preconditioners," SIAM J. Scientific Computing, Vol. 25, No. 2, 749-765, 2003.
18. Hsiao, G. C. and R. E. Kleinman, "Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics, " IEEE Transaction on Antennas and Propagation, Vol. 45, No. 3, 316-328, 1997.
19. "Multifrontal massively parallel solver," available online: http://www.enseeiht.fr/lima/apo/MUMPS.
20. Frayssé, V., L. Giraud, and S. Gratton, "A set of fiexibleGMRES routines for real and complex arithmetics," CERFACS Technical Report, TR/PA/98/20, available online: http://www.cerfacs.fr/algor/reports/ algo_reports_1998.html.
21. Brezzi, F. and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer-Verlag, 1991.
22. Engquist, B. and J.-C. Nédélec, "Effective boundary conditions for acoustic and electro-magnetics scattering in thin layers," research report CMAP, Ecole Polytechnique, Palaiseau, France, 1993.
23. Chew, W.-C., J. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.
24. Collino, F. and F. Millot, "2-components algorithm for the multilevel fast multipole method for solving large scale diffraction problems," JEE02 (European Symposium on Numerical Methods in Electromagnetics), Toulouse, France.
25. Collard, B., M'B. Fares, and B. Souny, "A new formulation for scattering by impedant 3D bodies," J. of Electromagn. Waves and Appl., Vol. 20, No. 10, 1291-1298, 2006.
26. Jung, B. H., T. K. Sarkar, and Y.-S. Chung, "A survey of various frequency domain integral equations for the analysis of scattering form three-dimensional dielectric objects," Progress In Electromagnetics Research, PIER 36, 193-246, 2002.
27. Zhou, X., "On Helmoltz's theorem and its interpretations," J. of Electromagn. Waves and Appl., Vol. 21, No. 4, 471-483, 2007.
28. Carpentieri, B., "Fast-iterative solution methods in electromagnetic scatteting," Progress In Electromagnetics Research, PIER 79, 151-178, 2008.
29. Bartoli and Bendali, "Robust and high-order effective boundary conditions for perfectly conducting scatterers," IMA J. Appl. Math., Vol. 67, 479-508, 2002.
30. Wang, D.-S., "Limits and validity of the impedance boundary condition on penetrable surfaces," IEEE Trans. Ant. Prop., Vol. 35, 453-457, October 1987.