Optimization algorithm to detect fine shape details from elastic moment tensors

Abstract

In this thesis we develop an iterative approach for reconstructing fine shape details of an inclusion using higher-order Elastic Moment Tensors (EMTs). It is known that the EMTs contain the information about the shape of an inclusion. Given an arbitrary inclusion, one can find an equivalent ellipse with same first order EMTs. To recover fine shape details of an inclusion, we derive an asymptotic formula for the perturbation in the EMTs that are due to small changes in the interface of the inclusion. For deriving the formula, we use the layer potential technique which is rigorous. Based on this formula, we propose an optimization algorithm to find fine shape details. We perform some numerical experiments to demonstrate the validity of the proposed method.