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The Fourier Singular Complement Method for the Poisson problem. Part II: axisymmetric domains

Patrick Ciarlet 1, 2 Beate Jung 3 Samir Kaddouri 1, 2 Simon Labrunie 4 Jun Zou 5
2 ONDES - Modeling, analysis and simulation of wave propagation phenomena
Inria Paris-Rocquencourt, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR2706
4 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : This paper is the second part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In the first part of this series, the Fourier Singular Complement Method was introduced and analysed, in prismatic domains. In this second part, the FSCM is studied in axisymmetric domains with conical vertices, whereas, in the third part, implementation issues, numerical tests and comparisons with other methods are carried out. The method is based on a Fourier expansion in the direction parallel to the reentrant edges of the domain, and on an improved variant of the Singular Complement Method in the 2D section perpendicular to those edges. Neither refinements near the reentrant edges or vertices of the domain, nor cut-off functions are required in the computations to achieve an optimal convergence order in terms of the mesh size and the number of Fourier modes used.
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Submitted on : Thursday, September 14, 2006 - 2:07:29 PM
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Patrick Ciarlet, Beate Jung, Samir Kaddouri, Simon Labrunie, Jun Zou. The Fourier Singular Complement Method for the Poisson problem. Part II: axisymmetric domains. Numerische Mathematik, Springer Verlag, 2006, 102, pp.583-610. ⟨10.1007/s00211-005-0664-8⟩. ⟨hal-00094298⟩

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