Convergence of Krylov subspace solvers with Schwarz preconditioner for the exterior Maxwell problem

Abstract : The consideration of an integral representation as an exact boundary condition for the finite element resolution of wave propagation problems in exterior domain induces algorithmic difficulties. In this paper, we are interested in the resolution of an exterior Maxwell problem in 3D. As a first step, we focus on the justification of an algorithm described in literature, using an interpretation as a Schwarz method. The study of the convergence indicates that it depends significantly on the thickness of the domain of computation. This analysis suggests the use of the finite element term of Schwarz method as a preconditioner for use of Krylov iterative solvers. An analytical study of the case of a spherical perfect conductor indicates the efficiency of such approach. The consideration of the preconditioner suggested by the Schwarz method leads to a superlinear convergence of the GMRES predicted by the analytical study and verified numerically.
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Eric Darrigrand, Nabil Gmati, Rania Rais. Convergence of Krylov subspace solvers with Schwarz preconditioner for the exterior Maxwell problem. Computers and Mathematics with Applications, Elsevier, In press, 74 (11), pp.2691-2709. ⟨10.1016/j.camwa.2017.08.027⟩. ⟨hal-01611138⟩

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