Fictitious domain method for an inverse problem in volcanoes

International audience An inverse problem applied to volcanology is studied. It consists in the determination of the pressure applied to a crack in order to fit observed ground deformations. The deformation of the volcano is assumed to be governed by a linear elasticity PDE. The direct problem is so...

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Main Authors: Bodart, Olivier, Cayol, Valérie, Dabaghi, Farshid, Koko, Jonas
Other Authors: Institut Camille Jordan Villeurbanne (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet Saint-Étienne (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université Jean Monnet Saint-Étienne (UJM), Laboratoire Magmas et Volcans (LMV), Institut national des sciences de l'Univers (INSU - CNRS)-Université Jean Monnet Saint-Étienne (UJM)-Institut de Recherche pour le Développement et la société-Université Clermont Auvergne 2017-2020 (UCA 2017-2020 )-Centre National de la Recherche Scientifique (CNRS)-Observatoire de Physique du Globe de Clermont-Ferrand (OPGC), Institut national des sciences de l'Univers (INSU - CNRS)-Université Clermont Auvergne 2017-2020 (UCA 2017-2020 )-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Clermont Auvergne 2017-2020 (UCA 2017-2020 )-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne 2017-2020 (UCA 2017-2020 ), French Government Laboratory of Excellence initiative no.ANR-10-LABX-0006, Haynes, R., MacLachlan, S., Cai, X.-C., Halpern, L., Kim, H.H., Klawonn, A., Widlund
Format: Book
Language:English
Published: HAL CCSD 2020
Subjects:
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
[SDU.STU.VO]Sciences of the Universe [physics]/Earth Sciences/Volcanology
Canada
Newfoundland
Online Access:https://hal.uca.fr/hal-02325032
https://hal.uca.fr/hal-02325032/document
https://hal.uca.fr/hal-02325032/file/BCDK_DD25_revised.pdf
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Summary:International audience An inverse problem applied to volcanology is studied. It consists in the determination of the pressure applied to a crack in order to fit observed ground deformations. The deformation of the volcano is assumed to be governed by a linear elasticity PDE. The direct problem is solved via a fictitious domain method, using a finite element discretization of XFEM type. The gradient of the cost function is derived from a Lagrangian. A numerical test is presented.

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