Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems

Nathalie Bartoli; Francis Collino

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 5, page 1023-1049
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bartoli, Nathalie, and Collino, Francis. "Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems ." ESAIM: Mathematical Modelling and Numerical Analysis 34.5 (2010): 1023-1049. <http://eudml.org/doc/197456>.

@article{Bartoli2010,
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. },
author = {Bartoli, Nathalie, Collino, Francis},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Integral equation; saddle point problems.; saddle point problems; radar cross section; integral equation; two-dimensional scattering; asymptotic analysis; algorithms; thin dielectric layer},
language = {eng},
month = {3},
number = {5},
pages = {1023-1049},
publisher = {EDP Sciences},
title = {Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems },
url = {http://eudml.org/doc/197456},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Bartoli, Nathalie
AU - Collino, Francis
TI - Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 5
SP - 1023
EP - 1049
AB - 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.
LA - eng
KW - Integral equation; saddle point problems.; saddle point problems; radar cross section; integral equation; two-dimensional scattering; asymptotic analysis; algorithms; thin dielectric layer
UR - http://eudml.org/doc/197456
ER -

References

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  10. D. Colton and R. Kress, in Inverse Acoustic and Electromagnetic Scattering Theory, 93, Springer-Verlag (1992).  
  11. B. Després, Quadractic functional and integral equations for harmonic wave problems in exterior domains. RAIRO-Modél. Math. Anal. Numér. 31 (1997) 679-732.  
  12. 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).  
  13. V. Girault and P.A. Raviart, in Finite Element methods for Navier-Stokes Equations, Theory and Algorithms, 5, Springer-Verlag (1986).  
  14. G.H. Golub and C.F. Van Loan, in Matrix Computations, 3rd edn., Chap. 9-10, The Johns Hopkins University Press, Baltimore (1996).  
  15. B. Perthame and L. Vega, Morrey-Campanato estimates for Helmholtz equations. J. Funct. Anal., 164 (1999) 340-355.  
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