Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides
| Autor: | Sonia Fliss, Antoine Tonnoir, Vahan Baronian, Anne-Sophie Bonnet-Ben Dhia |
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| Přispěvatelé: | Laboratoire d'Intégration des Systèmes et des Technologies (LIST), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Fliss, Sonia |
| Rok vydání: | 2016 |
| Předmět: |
Diffraction
Discretization Iterative method diffraction General Physics and Astronomy 01 natural sciences 010305 fluids & plasmas 0103 physical sciences [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Boundary value problem [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics modal expansion domain decomposition method Mathematics Applied Mathematics 010102 general mathematics Mathematical analysis Isotropy Domain decomposition methods Finite element method Computational Mathematics Modal Modeling and Simulation elastic waveguide iterative methods |
| Zdroj: | Wave Motion Wave Motion, Elsevier, 2016 Wave Motion, 2016 |
| ISSN: | 0165-2125 1878-433X |
| Popis: | International audience; We consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite straight isotropic elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with or without an overlap between the domains. Specific transmission conditions are used, so that only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using the Fraser bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized, in particular for the extension to the anisotropic case. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time. |
| Databáze: | OpenAIRE |
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