Construction et analyse de conditions absorbantes de type Dirichlet-to-Neumann pour des frontières ellipsoïdales

Anne-Gaëlle Saint-Guirons 1, 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : New approximate local DtN boundary conditions are proposed to be set on elliptical- or prolate-spheroidal exterior boundaries when solving respectively two- or three-dimensional acoustic scattering problems by elongated obstacles. These new absorbing conditions are designed to be exact for the first modes. They can be easily incorporated in any finite element parallel code while preserving the local structure of the algebraic system. moreover, since the proposed conditions are applicable to exterior elliptical-shaped boundaries that are more suitable for surrounding elongated scatterers, they yield to smaller computational domains which contributes to limit computational burden. In the low frequency regime, using an on-surface radiation condition formulation, we perform the mathematical and numerical analysis of the effect of the frequency and the eccentricity values of the boundary on the accuracy of these conditions, when applied for solving radiating and scattering problems (2D and 3D). It reveals - in particular - that the new second-order DtN boundary condition retains a very good level of accuracy regardless of the slenderness of the boundary. In the high frequency regime we study the volumic formulation of the problem. It shows that it is not necessary to consider a big computational domain around the scatterer to obtain accurate results with the new second-order local DtN condition. The high frequency analysis of the reflection coefficient shows that it tends to 0 for propagative modes and it converges exponentially towards 0 for a special class of propagative, grazing and evanescent modes.
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https://tel.archives-ouvertes.fr/tel-00356994
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Submitted on : Thursday, January 29, 2009 - 10:52:45 AM
Last modification on : Sunday, April 7, 2019 - 3:00:02 PM
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Anne-Gaëlle Saint-Guirons. Construction et analyse de conditions absorbantes de type Dirichlet-to-Neumann pour des frontières ellipsoïdales. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2008. Français. ⟨tel-00356994⟩

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