An Unpreconditioned Boundary-Integral for Iterative Solution of Scattering Problems with Non-Constant Leontovitch Impedance Boundary Conditions
D. Levadoux 1, F. Millot 2, S. Pernet 3*1 ONERA, French Aerospace Lab, Chemin de la humiere 91761 Palaiseau, France.
2 CERFACS 42 avenue G. Coriolis 31057 Toulouse, France.
3 ONERA, French Aerospace Lab, 2 Avenue Edouard Belin, 31000 Toulouse, France.
Received 25 March 2013; Accepted (in revised version) 28 October 2013
Available online 5 March 2014
This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition. It has two objectives. Firstly, the intrinsically well-conditioned integral equation (noted GCSIE) proposed in  is described focusing on its discretization. Secondly, we highlight the potential of this method by comparison with two other methods, the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasi-optimal for Lipschitz polyhedron, the second being a CFIE-like formulation . In particular, we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation. Finally, as expected, It is demonstrated that no preconditioner is needed for this formulation.AMS subject classifications: 65R20, 15A12, 65N38, 65F10, 65Z05
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Key words: Integral equation, boundary element method, impedance boundary equation, preconditioner, GMRES, fast multipole method.
Email: David.Levadoux@onera.fr (D. Levadoux), email@example.com (F. Millot), Sebastien.Pernet@onera.fr (S. Pernet)