UCLA

Numerical approaches for localization and shape quantification of multiple arbitrarily-shaped scatterers (cracks, voids, and inclusions) embedded in heterogenous linear elastic media are described. A dynamic extended finite element method (XFEM) equipped with scatterer-boundary parameterizations using cubic splines is used to solve the forward (wave propagation) problem. The said combination

enables the modeling of scatterer boundaries with complex geometries over a stationary background mesh. The inverse problem is cast as an optimization problem whereby an appropriate measure of the discrepancies between wave responses obtained from forward simulations and those that are measured from the actual specimen is minimized. A gradient-based minimization that is steered with a divide-alternate-and-conquer strategy serves as the inverse problem solver. The divide-and-conquer approach enables isolating the global minimizer among potentially multiple solutions, and the alternate-and-conquer approach enhances the former strategy to tackle multiple scatterers. The approaches developed herein are verified using using numerical experiments (i.e., synthetic data sets) involving different types of scatterers. Effects of measurement noise are also investigated.