Asymptotic models for scattering problems from unbounded media with high conductivity

Houssem Haddar (1) , Armin Lechleiter (1)

1 DeFI - Shape reconstruction and identification

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 numerical approximation of obtained GIBC (up to order 3) and numerically test theoretical convergence rates.

Mots clés: Scattering problems; unbounded domains; asymptotic models; generalized impedance boundary conditions; high conductivity

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Mathématiques générales [math.GM]

Houssem Haddar, Armin Lechleiter. Asymptotic models for scattering problems from unbounded media with high conductivity. [Research Report] RR-6841, INRIA. 2009, pp.29. ⟨inria-00360552⟩