Asymptotic behavior of acoustic waves scattered by very small obstacles
| Autor: | Sébastien Tordeux, Hélène Barucq, Julien Diaz, Vanessa Mattesi |
|---|---|
| Přispěvatelé: | Advanced 3D Numerical Modeling in Geophysics (Magique 3D), Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Montefiore - Département d'Electricité, Electronique et Informatique (Liège), Hélène Barucq and Julien Diaz have received funding from the European Union’s Horizon2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777778 (MATHROCKS). Vanessa Mattesi and Sébastien Tordeux have received funding from CERFACS and Nouvelle Aquitaine Region. |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Scattering problem
Direct numerical simulation 010103 numerical & computational mathematics 01 natural sciences Convergence (routing) Applied mathematics Time domain 0101 mathematics Méthode des développements asymptotiques raccordés Mellin transform Mathematics Laplace's equation Matched asymptotic expansion method Numerical Analysis Applied Mathematics Numerical analysis Transformée de Mellin Acoustic wave 010101 applied mathematics Computational Mathematics Singularity theory Théorie des singularités Modeling and Simulation Equation des ondes acoustique Asymptotic expansion Acoustic wave propagation Analysis Problème de diffraction [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | ESAIM: Mathematical Modelling and Numerical Analysis ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, In press, 55, pp.705-731. ⟨10.1051/m2an/2020047⟩ ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.705-731. ⟨10.1051/m2an/2020047⟩ |
| ISSN: | 0764-583X 1290-3841 |
| DOI: | 10.1051/m2an/2020047⟩ |
| Popis: | International audience; The direct numerical simulation of the acoustic wave scattering created by very small obstacles is very expensive, especially in three dimensions and even more so in time domain. The use of asymptotic models is very efficient and the purpose of this work is to provide a rigorous justification of a new asymptotic model for low-cost numerical simulations. This model is based on asymptotic near-field and far-field developments that are then matched by a key procedure that we describe and demonstrate. We show that it is enough to focus on the regular part of the wave field to rigorously establish the complete asymptotic expansion. For that purpose, we provide an error estimate which is set in the whole space, includingthe transition region separating the near-field from the far-field area. The proof of convergence is established through Kondratiev’s seminal work on the Laplace equation and involves the Mellin transform. Numerical experiments including multiple scattering illustrate the efficiency of the resulting numerical method by delivering some comparisons with solutions computed with a finite element software. |
| Databáze: | OpenAIRE |
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