Identification of a scatterer embedded in elastic heterogeneous media using dynamic XFEM

A numerical approach for identifying a scatterer embedded in elastic heterogeneous media is described. This scatterer may be a crack, a void, or an inclusion with properties that have detectable contrasts from those of the host medium. The forward (wave propagation) problem is solved using the dynamic extended finite element method (XFEM), which allows the boundary of the scatterer to be easily relocated over a stationary background mesh. The inverse problem is cast as a minimization problem whereby the unknown shape parameters of the scatterer—e.g., a line crack’s center coordinates, size, and orientation—are the updating parameters. A gradient-based method is utilized to solve the minimization problem. In order to alleviate the potential manifestation of multiple solutions to the inverse problem, various deployment patterns for multiple sensors are investigated, and also a divide-and-conquer approach is adopted, wherein a set of independent inversions using multiple initial guesses are carried out.