Qualitative indicator functions for imaging crack networks using acoustic waves
| Autor: | Lucas Chesnel, Lorenzo Audibert, Houssem Haddar, Kevish Napal |
|---|---|
| Přispěvatelé: | Performance, Risque Industriel, Surveillance pour la Maintenance et l’Exploitation (EDF R&D PRISME), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Inversion of Differential Equations For Imaging and physiX (IDEFIX), 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)-École polytechnique (X)-EDF (EDF), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Department of Civil and Environmental Engineering [Fort Collins], Colorado State University [Fort Collins] (CSU), Shape reconstruction and identification (DeFI ), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Generalized linear sampling method
Spectral signature Applied Mathematics Plane wave Near and far field 010103 numerical & computational mathematics Acoustic wave 01 natural sciences Computational Mathematics Mathematics - Analysis of PDEs Indicator function Transmission (telecommunications) Homogeneous FOS: Mathematics interior transmission problem [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] cracks 0101 mathematics Differential (infinitesimal) artificial background Algorithm Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing SIAM Journal on Scientific Computing, 2021, ⟨10.1137/20M134650X⟩ SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2021 |
| ISSN: | 1064-8275 |
| Popis: | International audience; We consider the problem of imaging a crack network embedded in some homogeneous background from measured multi-static far field data generated by acoustic plane waves. We propose two novel approaches that can be seen as extensions of linear sampling-type methods and that provide indicator functions which are sensitive to local cracks densities. The first approach uses multiple frequencies data to compute spectral signatures associated with artificially embedded localized obstacles. The second approach also exploits the idea of incorporating an artificial background but uses data for a single frequency. The indicator function is built using a similar concept as for differential sampling methods: compare the solution of the interior transmission problem for healthy inclusion with the one with embedded cracks. The performance of the methods is tested and discussed on synthetic examples and the numerical results are compared with the ones obtained using the classical factorization method. |
| Databáze: | OpenAIRE |
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