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The Fourier Singular Complement Method for the Poisson problem. Part I: prismatic domains

Patrick Ciarlet 1 Beate Jung 2 Samir Kaddouri 3 Simon Labrunie 4 Jun Zou 5
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
3 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
Abstract : This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed, in prismatic domains. In the 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 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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https://hal.archives-ouvertes.fr/hal-00094285
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Submitted on : Thursday, September 14, 2006 - 2:01:28 PM
Last modification on : Wednesday, November 3, 2021 - 3:10:04 AM
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Patrick Ciarlet, Beate Jung, Samir Kaddouri, Simon Labrunie, Jun Zou. The Fourier Singular Complement Method for the Poisson problem. Part I: prismatic domains. Numerische Mathematik, Springer Verlag, 2005, 101, pp.423-450. ⟨10.1007/s00211-005-0621-6⟩. ⟨hal-00094285⟩

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