دورية أكاديمية
Asymptotic behavior of acoustic waves scattered by very small obstacles
| العنوان: | Asymptotic behavior of acoustic waves scattered by very small obstacles |
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| المؤلفون: | Barucq, Hélène, Diaz, Julien, Mattesi, Vanessa, Tordeux, Sebastien |
| المصدر: | ESAIM: Mathematical Modelling and Numerical Analysis, 55, S705 - S731 (2021) |
| بيانات النشر: | EDP Sciences, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Acoustic wave propagation, Matched asymptotic expansion method, Mellin transform, Scattering problem, Singularity theory, Asymptotic behaviors, Asymptotic expansion, Asymptotic model, Finite element software, Numerical experiments, Three dimensions, Transition regions, Analysis, Numerical Analysis, Modeling and Simulation, Computational Mathematics, Applied Mathematics, Physical, chemical, mathematical & earth Sciences, Mathematics, Engineering, computing & technology, Computer science, Physique, chimie, mathématiques & sciences de la terre, Mathématiques, Ingénierie, informatique & technologie, Sciences informatiques |
| الوصف: | 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, including the 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. |
| نوع الوثيقة: | journal article http://purl.org/coar/resource_type/c_6501Test article peer reviewed |
| اللغة: | English |
| العلاقة: | https://www.esaim-m2an.org/10.1051/m2an/2020047/pdfTest; urn:issn:0764-583X; urn:issn:1290-3841 |
| DOI: | 10.1051/m2an/2020047 |
| الوصول الحر: | https://orbi.uliege.be/handle/2268/294097Test |
| حقوق: | open access http://purl.org/coar/access_right/c_abf2Test info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsorb.294097 |
| قاعدة البيانات: | ORBi |
| DOI: | 10.1051/m2an/2020047 |
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