XFEM-Based Fictitious Domain Method for Linear Elasticity Model with Crack

Abstract

International audienc

Fictitious Domain Method for an Inverse Problem in Volcanoes

“…To solve the direct problem (1), we use a domain decomposition method. More precisely, following [1], the domain Ω is split into two subdomains such that each point of the domain lies on one side of the crack or on the crack. Moreover, the global unknown solution u is decoupled in two sub-solutions for each side of the crack.…”

“…The two last conditions in (4) enforce the continuity of displacement and stress across Γ 0 . Notice that the boundary conditions on Γ 0 ensure the construction of a global displacement field in H 1 (Ω \ Γ C ) solving the original problem (1). Let us define the following Hilbert spaces…”

“…Therefore, it is straightforward to prove the existence and uniqueness of a solution to Problem (5) (see e.g. [1] ans references within).…”

“…Using a domain decomposition technique then appears as the natural solution to these problems. In [1], a first step was made with the development of a direct solver implementing a domain decomposition method. The present work represents a step further with the use of such a solver, which has been improved since the publication of [1], to solve inverse problems in the field of earth sciences.…”

“…In [1], a first step was made with the development of a direct solver implementing a domain decomposition method. The present work represents a step further with the use of such a solver, which has been improved since the publication of [1], to solve inverse problems in the field of earth sciences. To our knowledge, this is the first work using these kind of techniques in this field of application.…”