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

An inverse problem applied to volcanology is studied. It consists in the determination of variable pressure a crack order fit observed ground displacements. The deformation volcano assumed be governed by linear elasticity. direct solved via fictitious domain method, using finite element discretization XFEM type. misfit minimized combination decomposition and optimatily conditions. gradient cost function derived from sensitivity analysis. Discretization Numerical tests (in 2D 3D) are presented illustrate effectiveness proposed approach. In particular, we find that quasi-Newton method more efficient than conjugate for solving optimization problem.