A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 4, p. 781-801

The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.

DOI : https://doi.org/10.1051/m2an/2010023
Classification:  65R20,  15A12,  65N38,  65F10,  65Z05
Keywords: electromagnetic scattering, boundary integral equations, impedance boundary condition, preconditioner
@article{M2AN_2010__44_4_781_0,
     author = {Pernet, S\'ebastien},
     title = {A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {4},
     year = {2010},
     pages = {781-801},
     doi = {10.1051/m2an/2010023},
     zbl = {1205.78025},
     mrnumber = {2683583},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_4_781_0}
}
Pernet, Sébastien. A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 4, pp. 781-801. doi : 10.1051/m2an/2010023. http://www.numdam.org/item/M2AN_2010__44_4_781_0/

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