%0 Journal Article %T An inverse problem in an elastic domain with a crack : a fictitious domain approach %+ Institut Camille Jordan (ICJ) %+ Modélisation mathématique, calcul scientifique (MMCS) %+ Laboratoire Magmas et Volcans (LMV) %+ Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS) %A Bodart, Oliver %A Cayol, Valérie %A Dabaghi, Farshid %A Koko, Jonas %< avec comité de lecture %Z Challenge 4 %@ 1420-0597 %J Computational Geosciences %I Springer Verlag %8 2022-01-07 %D 2022 %R 10.1007/s10596-021-10121-7 %K Inverse problem %K Crack %K Fictitious domain %K Linear elasticity %K Conjugate gradient %Z Sciences of the Universe [physics]/Earth Sciences/VolcanologyJournal articles %X An inverse problem applied to volcanology is studied. It consists in the determination of the variable pressure applied to a crack in order to fit observed ground displacements. The deformation of the volcano is assumed to be governed by linear elasticity. The direct problem is solved via a fictitious domain method, using a finite element discretization of XFEM type. The ground misfit is minimized using a combination of a domain decomposition and optimatily conditions. The gradient of the cost function is derived from a sensitivity analysis. Discretization of the problem is studied. Numerical tests (in 2D and 3D) are presented to illustrate the effectiveness of the proposed approach. In particular, we find that a quasi-Newton method is more efficient than a conjugate gradient method for solving the optimization problem. %G English %2 https://uca.hal.science/hal-03524275/document %2 https://uca.hal.science/hal-03524275/file/BodartCayolDabaghiKoko_post-print.pdf %L hal-03524275 %U https://uca.hal.science/hal-03524275 %~ UNIV-ST-ETIENNE %~ IRD %~ INSU %~ PRES_CLERMONT %~ CNRS %~ ICJ %~ UNIV-LYON1 %~ INSA-LYON %~ EC-LYON %~ LMV %~ LIMOS %~ ACL-SF %~ OPGC %~ INSA-GROUPE %~ CAP20-25 %~ UDL %~ UNIV-LYON %~ ANR %~ CLERMONT-AUVERGNE-INP %~ TEST3-HALCNRS