Geodesic
A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 4, pp. 781-801

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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 : 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 },
     pages = {781--801},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {4},
     year = {2010},
     doi = {10.1051/m2an/2010023},
     mrnumber = {2683583},
     zbl = {1205.78025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010023/}
}
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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 , Tome 44 (2010) no. 4, pp. 781-801. doi: 10.1051/m2an/2010023

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