Asymptotic models for scattering from unbounded media with high conductivity
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 6, pp. 1295-1317.

We analyze the accuracy and well-posedness of generalized impedance boundary value problems in the framework of scattering problems from unbounded highly absorbing media. We restrict ourselves in this first work to the scalar problem (E-mode for electromagnetic scattering problems). Compared to earlier works, the unboundedness of the rough absorbing layer introduces severe difficulties in the analysis for the generalized impedance boundary conditions, since classical compactness arguments are no longer possible. Our new analysis is based on the use of Rellich-type estimates and boundedness of L2 solution operators. We also discuss some numerical experiments concerning these boundary conditions.

DOI : 10.1051/m2an/2010029
Classification : 35C20, 78A40
Mots-clés : scattering problems, unbounded domains, asymptotic models, generalized impedance boundary conditions, high conductivity 
@article{M2AN_2010__44_6_1295_0,
     author = {Haddar, Houssem and Lechleiter, Armin},
     title = {Asymptotic models for scattering from unbounded media with high conductivity},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1295--1317},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {6},
     year = {2010},
     doi = {10.1051/m2an/2010029},
     mrnumber = {2769059},
     zbl = {1206.35066},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2010029/}
}
TY  - JOUR
AU  - Haddar, Houssem
AU  - Lechleiter, Armin
TI  - Asymptotic models for scattering from unbounded media with high conductivity
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2010
SP  - 1295
EP  - 1317
VL  - 44
IS  - 6
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/m2an/2010029/
DO  - 10.1051/m2an/2010029
LA  - en
ID  - M2AN_2010__44_6_1295_0
ER  - 
%0 Journal Article
%A Haddar, Houssem
%A Lechleiter, Armin
%T Asymptotic models for scattering from unbounded media with high conductivity
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2010
%P 1295-1317
%V 44
%N 6
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/m2an/2010029/
%R 10.1051/m2an/2010029
%G en
%F M2AN_2010__44_6_1295_0
Haddar, Houssem; Lechleiter, Armin. Asymptotic models for scattering from unbounded media with high conductivity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 44 (2010) no. 6, pp. 1295-1317. doi : 10.1051/m2an/2010029. http://www.numdam.org/articles/10.1051/m2an/2010029/

[1] M. Artola and M. Cessenat, Diffraction d'une onde électromagnétique par un obstacle borné à permittivité et perméabilité élevées. C. R. Acad. Sci. Paris Sér. I Math. 314 (1992) 349-354. | Zbl

[2] S.N. Chandler-Wilde and P. Monk, Existence, uniqueness, and variational methods for scattering by unbounded rough surfaces. SIAM. J. Math. Anal. 37 (2005) 598-618. | Zbl

[3] S.N. Chandler-Wilde and P. Monk, The pml for rough surface scattering. Appl. Numer. Math. 59 (2009) 2131-2154.

[4] S.N. Chandler-Wilde and C.R. Ross, Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane. Math. Meth. Appl. Sci. 19 (1996) 959-976. | Zbl

[5] S.N. Chandler-Wilde, E. Heinemeyer and R. Potthast, Acoustic scattering by mildly rough surfaces in three dimensions. SIAM J. Appl. Math. 66 (2006) 1002-1026. | Zbl

[6] S.N. Chandler-Wilde, P. Monk and M. Thomas, The mathematics of scattering by unbounded, rough, inhomogeneous layers. J. Comput. Appl. Math. 204 (2007) 549-559. | Zbl

[7] P. Cummings and X. Feng, Sharp regularity coefficient estimates for complex-valued acoustic and elastic Helmholtz equations. Math. Mod. Meth. Appl. Sci. 16 (2006) 139-160. | Zbl

[8] M. Duruflé, H. Haddar and P. Joly, Higher order generalized impedance boundary conditions in electromagnetic scattering problems. C. R. Phys. 7 (2006) 533-542.

[9] H. Haddar, P. Joly and H.-M. Nguyen, Generalized impedance boundary conditions for scattering by strongly absorbing obstacles: the scalar case. Math. Mod. Meth. Appl. Sci. 15 (2005) 1273-1300. | Zbl

[10] F. Ihlenburg, Finite element analysis of acoustic scattering. Springer (1998). | Zbl

[11] A. Lechleiter and S. Ritterbusch, A variational method for wave scattering from penetrable rough layers. IMA J. Appl. Math. (2009) doi:10.1093/imamat/hxp040. | Zbl

[12] W. Mclean, Strongly Elliptic Systems and Boundary Integral Operators. Cambridge University Press, Cambridge (2000). | Zbl

[13] J.C. Nédélec, Acoustic and electromagnetic equations, Applied Mathematical Sciences 144. Springer-Verlag, Berlin (2001). | Zbl

[14] S.M. Rytov, Calcul du skin-effet par la méthode des perturbations. J. Phys. USSR 2 (1940) 233-242. | JFM

[15] T.B.A. Senior and J.L. Volakis, Approximate boundary conditions in electromagnetics, IEE Electromagnetic waves series 41. The institution of Electrical Engineers, London (1995). | Zbl

[16] B. Zhang and S.N. Chandler-Wilde, Integral equation methods for scattering by infinite rough surfaces. Math. Meth. Appl. Sci. 26 (2003) 463-488. | Zbl

Cité par Sources :