On the Kleinman-Martin integral equation method for electromagnetic scattering by a dielectric body*

SIAM Journal on Applied Mathematics

Volumn 71, Issue 2, 2011, Pages 635-656

  Costabel, Martin ^a   Le Louër, Frédérique ^a  

^a UNIVERSITÉ DE RENNES 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE SCATTERING; BOUNDARY INTEGRAL EQUATIONS; BOUNDARY VALUE PROBLEMS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC WAVE SCATTERING; ELECTROMAGNETIC WAVES;

ACOUSTIC SCATTERING PROBLEM; BOUNDARY INTEGRAL FORMULATIONS; DIELECTRIC SCATTERING; ELECTROMAGNETIC SCATTERING; INTEGRAL EQUATION METHODS; INTERFACE PROBLEMS; MAGNETIC CURRENT DENSITY; SINGLE INTEGRAL EQUATIONS;

MAXWELL EQUATIONS;

EID: 79957473486     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/090779462     Document Type: Article

References (34)

1. F. P. Andriulli, K. Cools, H. Bagci, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, A multiplicative Calderon preconditioner for electric field integral equation, IEEE Trans. Antennas and Propagation, 56 (2008), pp. 2398-2412.
2. A. Buffa and P. Ciarlet, Jr., On traces for functional spaces related to Maxwell's equations. I. An integration by parts formula in Lipschitz polyhedra, Math. Methods Appl. Sci., 24 (2001), pp. 9-30. (Pubitemid 32270777)
3. A. Buffa and P. Ciarlet, Jr., On traces for functional spaces related to Maxwell's equations. II. Hodge decompositions on the boundary of Lipschitz polyhedra and applications, Math. Methods Appl. Sci., 24 (2001), pp. 31-48.
4. A. Buffa, M. Costabel, and C. Schwab, Boundary element methods for Maxwell's equations on non-smooth domains, Numer. Math., 92 (2002), pp. 679-710. (Pubitemid 36161590)
5. A. Buffa, M. Costabel, and D. Sheen, On traces for H(curl, O) in Lipschitz domains, J. Math. Anal. Appl., 276 (2002), pp. 845-867.
6. A. Buffa and R. Hiptmair, A coercive combined field integral equation for electromagnetic scattering, SIAM J. Numer. Anal., 42 (2004), pp. 621-640. (Pubitemid 40645208)
7. A. Buffa, R. Hiptmair, T. von Petersdorff, and C. Schwab, Boundary element methods for Maxwell transmission problems in Lipschitz domains, Numer. Math., 95 (2003), pp. 459-485. (Pubitemid 37513715)
8. M. Cessenat, Mathematical Methods in Electromagnetism. Linear Theory and Applications, Ser. Adv. Math. Appl. Sci. 41, World Scientific, River Edge, NJ, 1996.
9. D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Pure Appl. Math. (N. Y.), John Wiley & Sons, New York, 1983.
10. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd ed., Appl. Math. Sci. 93, Springer-Verlag, Berlin, 1998.
11. M. Costabel, Boundary integral operators on Lipschitz domains: Elementary results, SIAM J. Math. Anal., 19 (1988), pp. 613-626.
12. M. Costabel and F. Le Louër, On domain derivatives of the solution to the electromagnetic transmission problem, Oberwolfach Rep., 19 (2008), pp. 967-969.
13. M. Costabel and F. Le Louër, On the Kleinman-Martin integral equation method for the electromagnetic scattering problem by a dielectric, in Proceedings of the 9th International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2009.
14. M. Costabel and E. P. Stephan, Strongly elliptic boundary integral equations for electromagnetic transmission problems, Proc. Roy. Soc. Edinburgh Sect. A, 109 (1988), pp. 271-296.
15. div (Γ) et nature de l'opérateur de Steklov- Poincaré du problème extérieur de l'é lectromagnétisme, C. R. Acad. Sci. Paris Sér. I Math., 316 (1993), pp. 369-372.
16. R. F. Harrington, Boundary integral formulations for homogeneous materials bodies, J. Electromagn. Waves Appl., 3 (1989), pp. 1-15.
17. G. C. Hsiao and W. L. Wendland, Boundary Integral Equations, Appl. Math. Sci. 164, Springer-Verlag, Berlin, 2008.
18. D. Jerison and C. E. Kenig, The inhomogeneous Dirichlet problem in Lipschitz domains, J. Funct. Anal., 130 (1995), pp. 161-219.
19. R. E. Kleinman and P. A. Martin, On single integral equations for the transmission problem of acoustics, SIAM J. Appl. Math., 48 (1988), pp. 307-325.
20. R. Kress, Linear Integral Equations, 2nd ed., Appl. Math. Sci. 82, Springer-Verlag, New York, 1999.
21. F. Le Louër, Optimisation de formes d'antennes lentilles intégrées aux ondes millimétriques, Ph.D. in Numerical Analysis, Université de Rennes 1, Rennes, France, 2009; available online from http://tel.archives-ouvertes.fr/tel-00421863/fr/.
22. P. A. Martin and P. Ola, Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), pp. 185-208.
23. E. Marx, Integral equation for scattering by a dielectric, IEEE Trans. Antennas and Propagation, 32 (1984), pp. 166-172.
24. J. R. Mautz, A stable integral equation for electromagnetic scattering from homogeneous dielectric bodies, IEEE Trans. Antennas and Propagation, 37 (1989), pp. 1070-1071.
25. D. Mitrea and M. Mitrea, Finite energy solutions of Maxwell's equations and constructive Hodge decompositions on nonsmooth Riemannian manifolds, J. Funct. Anal., 190 (2002), pp. 339-417.
26. P. Monk, Finite Element Methods for Maxwell's Equations, Numer. Math. Sci. Comput., Oxford University Press, New York, 2003.
27. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, New York, Heidelberg, 1969.
28. J.-C. Nédélec, Acoustic and Electromagnetic Equations: Integral Representations for Harmonic Problems, Appl. Math. Sci. 144, Springer-Verlag, New York, 2001.
29. A. Pomp, The integral method for coated gratings: Computational cost, J. Modern Opt., 38 (1991), pp. 109-120.
30. F. Seydou, R. Duraiswami, N. A. Gumerov, and T. Seppänen, TM electromagnetic scattering from multilayered dielectric bodies-Numerical solution, ACES J., 19 (2004), pp. 100-107.
31. O. Steinbach and M.Windisch, Modified combined field integral equations for electromagnetic scattering, SIAM J. Numer. Anal., 47 (2009), pp. 1149-1167.
32. D. R. Swatek and I. R. Ciric, Reduction of multiply-nested dielectric bodies for wave scattering analysis by single source surface integral equations, J. Electromagn. Waves Appl., 14 (2000), pp. 405-422. (Pubitemid 30581477)
33. F. Valdès, F. P. Andriulli, H. Bagci, and E. Michielssen, On the regularization of single source combined integral equations for analyzing scattering from homogeneous penetrable objects, in Proceedings of the IEEE Antennas and Propagation Society International Symposium, 2009, pp. 1-4.
34. M. S. Yeung, Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects, IEEE Trans. Antennas and Propagation, 47 (1999), pp. 1615-1622. (Pubitemid 30536114)