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An inverse problem in an elastic domain with a crack : a fictitious domain approach

Abstract : 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.
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Submitted on : Thursday, January 13, 2022 - 10:50:43 AM
Last modification on : Thursday, January 20, 2022 - 3:38:14 AM
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Oliver Bodart, Valérie Cayol, Farshid Dabaghi, Jonas Koko. An inverse problem in an elastic domain with a crack : a fictitious domain approach. Computational Geosciences, Springer Verlag, 2022, ⟨10.1007/s10596-021-10121-7⟩. ⟨hal-03524275⟩



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