Commun. Comput. Phys., 15 (2014), pp. 1431-1460.

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 [30] 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 [14]. 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.

*Corresponding author.
Email: (D. Levadoux), (F. Millot), (S. Pernet)

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