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Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems

Published online by Cambridge University Press:  15 April 2002

Nathalie Bartoli  and
Francis Collino
Nathalie Bartoli
Affiliation:
CERFACS, 42 Av. G. Coriolis, 31057 Toulouse, France. UMR MIP INSA-CNRS-UPS, Insa de Toulouse, Département de Génie Mathématique, Toulouse, France.
Francis Collino
Affiliation:
CERFACS, 42 Av. G. Coriolis, 31057 Toulouse, France.
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Abstract

A new system of integral equations for the exterior 2D time harmonic scattering problem is investigated. This system was first proposed by B. Després in [11]. Two new derivations of this system are given: one from elementary manipulations of classical equations, the other based on a minimization of a quadratic functional. Numerical issues are addressed to investigate the potential of the method.

Keywords

Integral equationsaddle point problems.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 5 , September 2000 , pp. 1023 - 1049
Copyright
© EDP Sciences, SMAI, 2000

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References

M. Abramowitz and I.A. Stegun, Handbook of mathematical functions. Dover Publications, New-York (1972).
N. Bartoli, Higher Order Effective Boundary Conditions for Perfectly Conducting Scatterers Coated by a thin Dielectric Layer. PhD thesis, INSA, Toulouse (to appear).
N. Bartoli and A. Bendali, Higher order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer and their boundary element solution (to be submitted).
A. Bendali, Boundary element solution of scattering problems relative to a generalized impedance boundary condition, in Partial differential equations, Theory and numerical solution, W. Jäger, J. Necas, O. John, K. Najzar and J. Stará, Eds. Chapman & Hall/CRC, 406 (1999) 10-24.
Bendali, A. and Vernhet, L., Résolution par élements finis de frontière d'un problème de diffraction d'onde comportant une condition aux limites d'impédance généralisée. C. R. Acad. Sci. Paris , 321 (1995) 791-797.
F. Brezzi and M. Fortin, in Mixed and Hybrid Finite Element Method, volume 15, Springer-Verlag (1991).
D. Calvetti, L. Reichel and Q. Zhang, Conjugate gradient algorithms for symmetric inconsistent linear systems. in Proceedings of the Cornelius Lanczos International Centenary Conference, J.D. Brown, M.T. Chu, D.C. Ellison and R.J. Plemmons, Eds. SIAM, Philadelphia (1994) 267-272.
G. Chen and J. Zhou, in Boundary element Methods. Academic Press, London (1992).
F. Collino and B. Després, Integral equations via saddle point problems for time-harmonic Maxwell's equations. SIAM J. Appl. Math. (submitted).
D. Colton and R. Kress, in Inverse Acoustic and Electromagnetic Scattering Theory, 93, Springer-Verlag (1992).
B. Després, Quadractic functional and integral equations for harmonic wave problems in exterior domains. RAIRO-Modél. Math. Anal. Numér. 31 (1997) 679-732.
V. Frayssé, L. Giraud and S. Gratton, A set of GMRES routines for real and complex arithmetics. Technical report, Cerfacs TR/PA/97/49, Toulouse, France (1997).
V. Girault and P.A. Raviart, in Finite Element methods for Navier-Stokes Equations, Theory and Algorithms, 5, Springer-Verlag (1986).
G.H. Golub and C.F. Van Loan, in Matrix Computations, 3rd edn., Chap. 9-10, The Johns Hopkins University Press, Baltimore (1996).
Perthame, B. and Vega, L., Morrey-Campanato estimates for Helmholtz equations. J. Funct. Anal. , 164 (1999) 340-355. CrossRef
Y. Saad, in Iterative methods for sparse linear systems. PWS publishing (1995).