Modeling and identification of an arbitrarily shaped scatterer using dynamic XFEM with cubic splines

Localization and shape identification of an arbitrarily shaped scatterer embedded in elastic heterogeneous media is investigated using the dynamic eXtended Finite Element Method (XFEM). The scatterer’s geometry is represented using cubic splines whose parameters are adaptively updated in a gradient-based minimization framework that is used to solve the inverse identification problem. The dynamic XFEM is employed to solve the forward (wave propagation) problem, because it enables direct parametric modeling of the moving boundary of the scatterer over a stationary background mesh. The use of open/close cubic splines combined with XFEM enables the effective construction of the complicated scatterer geometry by minimizing the number of unknown shape parameters. A two-phase divide-and-conquer approach is adopted to alleviate complications due to the potential manifestation of multiple solutions to the inverse problem and for increased computational efficiency. In first phase, the scatterer is localized using a simple geometric representation; and the search is carried out using multiple independent inversions starting from different initial estimates. Incidentally, this strategy is perfectly scalable in parallel computation. In the second phase, the geometric representation is adaptively refined using cubic splines to obtain an accurate estimate of the scatterer’s shape. Several numerical experiments are provided, which clearly show that the proposed approach is robust and can yield highly accurate results.