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A divide-alternate-and-conquer approach for localization and shape identification of multiple scatterers in heterogeneous media using dynamic XFEM

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  • A numerical method for localization and identification of multiple arbitrarily-shaped scatterers (cracks, voids, or inclusions) embedded within heterogeneous linear elastic media is described. An elastodynamic implementation of the extended finite element method (XFEM), which is endowed with a spline-based parameterization of the scatterer boundaries, is employed to solve the forward (wave propagation) problem. This particular combination enables direct, sensitivity-based, and computationally efficient manipulation of the scatterers' boundaries over a stationary background mesh during the inversion process. The inverse problem is cast as a formal optimization problem whereby the discrepancy between the measured wave responses and those from the estimated scatterers is minimized. The solution is achieved through a gradient-based procedure that is steered by a divide-alternate-and-conquer strategy. The divide-and-conquer segment of the search algorithm seeks the global minimizer among potentially multiple solutions, whereas the alternate-and-conquer segment adaptively refines the shapes of identified scatterers. The results of several synthetic experiments with various types of scatterers are provided. These experiments verify the overall approach, and demonstrate that it is robust, accurate, and effective even at high levels of measurement noise.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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