A stable well-conditioned integral equation for electromagnetism scattering

Journal of Computational and Applied Mathematics

Volumn 204, Issue 2 SPEC. ISS., 2007, Pages 440-451

  Alouges, F ^a   Borel, S ^b   Levadoux, D P ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b ONERA   (France)

Author keywords

CFIE; Helmholtz decomposition; Integral equation; Iterative method; Maxwell equations; Preconditioner; Time harmonic scattering problem

Indexed keywords

ELECTROMAGNETIC WAVE SCATTERING; HELMHOLTZ EQUATION; ITERATIVE METHODS; LINEAR EQUATIONS; MAXWELL EQUATIONS;

CFIE; HELMHOLTZ DECOMPOSITION; PRECONDITIONER; TIME-HARMONIC SCATTERING PROBLEM;

INTEGRAL EQUATIONS;

EID: 34247271927     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.02.049     Document Type: Article

References (27)

1. Antoine X., and Darbas M. Alternative integral equations for the iterative solution of acoustic scattering problems. Quart. J. Mech. Appl. Math. 58 1 (2005) 107-128
2. Barka A., Soudais P., and Volpert D. Scattering from 3-D cavities with a plug and play numerical scheme combining IE, PDI, and modal techniques. IEEE Trans. Antennas and Propagation 48 5 (2000) 704-712
3. A. Bendali, Approximation par éléments finis de surface de problèmes de diffraction des ondes électromagnétiques, Ph.D. Thesis, École Polytechnique, 1984.
4. S. Borel, Étude d'une équation intégrale stabilisée pour la résolution itérative de problèmes de diffractions d'ondes harmoniques en électromagnétisme, Ph.D. Thesis, Université Paris XI, 2006.
5. Borel S., Levadoux D.P., and Alouges F. A new well-conditioned integral formulation for Maxwell equations in three dimensions. IEEE Trans. Antennas and Propagation 53 9 (2005) 2995-3004
6. Brakhage A., and Werner P. Über das dirichletsche aussenraumproblem für die Helmholtzsche schwingungsgleichung. Arch. Math. 16 (1965) 325-329
7. Cessenat M. Mathematical Methods in Electromagnetism, Linear Theory and Applications (1996), World Scientific Publishing Co., River Edge, NJ
8. Christiansen S.H., and Nédélec J.-C. A preconditioner for the electric field integral equation based on Calderón formulas. SIAM J. Num. Anal. 40 3 (2002) 1100-1135
9. Colton D., and Kress R. Inverse Acoustic and Electromagnetic Scattering Theory (1992), Springer, Berlin
10. H. Contopanagos, D. Dembart, M. Epton, J.J. Ottusch, V. Rokhlin, J. Visher, S. Vandzura, Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering, Technical Report, Yale University, YALEU/DCS/RR-1198, June 2000.
11. M. Darbas, Préconditionneurs analytiques de type Calderón pour les formulations intégrales des problèmes de diffraction d'ondes, Ph.D. Thesis, Université Paul-Sabatier, 2004.
12. Greengard L., and Rokhlin V. A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica 6 (1997) 229-269
13. Heisenstat S.C., Helman H.C., and Schultz M.H. Variational iterative methods for nonsymmetric systems of linear equations. SIAM J. Num. Anal. 20 (1983) 345-357
14. Kupradze V.D. Potential Methods in the Theory of Elasticity (1965), Israel Program for Scientific Translations, Jerusalem
15. D.P. Levadoux, Étude d'une équation intégrale adaptée à la résolution hautes fréquences de l'équation de Helmholtz, Ph.D. Thesis, Université Paris VI, 2001.
16. Levadoux D.P. Proposition de préconditionneurs pseudo-différentiels pour l'équation CFIE de l'électromagnétisme. ESAIM: M2AN 39 1 (2005) 147-155
17. Levadoux D.P., and Michielsen B.L. Analysis of a boundary integral equation for high frequency Helmholtz problems. Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation (1-5 June, 1998), Golden, Colorado 765-767
18. Levadoux D.P., and Michielsen B.L. A new class of integral equations for scattering problems. Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (June 30-July 4, 2003), Jyvaskyla, Finland
19. Mautz J.R., and Harrington R.F. A combined-source solution for radiation and scattering from a perfectly conducting body. IEEE Trans. Antennas and Propagation AP-27 4 (1979) 445-454
20. McLean W., and Tran T. A preconditioning strategy for boundary element galerkin methods. Numer. Methods Partial Differential Equations 13 (1997) 283-301
21. K.M. Mitzner, Numerical solution of the exterior scattering problem at eigenfrequencies of the interior problem, International Scientific Radio Union Meeting, Boston, Mass., Mar. 1968.
22. Panich O.I. On the question of the solvability of the exterior boundary problem for the wave equation and Maxwell's equation (in Russian). Uspekhi Mat. Nauk. 20 1 (1965) 221-226
23. P.A. Raviart, J.-M. Thomas, A mixed finite element method for second order elliptic problems, in: I. Galligani, E. Magenes (Eds.), Mathematical Aspects of the Finite Element Method, Lecture Notes in Mathematics, vol. 606, Springer, Berlin, 1975, pp. 292-315.
24. Rokhlin V. Diagonal form of translation operators for the Helmholtz equation in three dimensions. Appl. Comput. Harmon. Anal. 1 (1993) 82-93
25. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Statist. Comput. 7 3 (1986) 856-869
26. O. Steinbach, Gebietzerlegungsmethoden mit Randintegralgleichungen und effiziente numerische Lösungsverfahren für gemischte Randwertprobleme, Ph.D. Thesis, University of Stuttgard, 1996.
27. Steinbach O., and Wendland W.L. The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9 1-2 (1998) 191-216