Detection of holes in an elastic body based on eigenvalues and traces of eigenmodes

We consider the numerical solution of an inverse problem of finding the shape and location of holes in an elastic body. The problem is solved by minimizing a functional depending on the eigenvalues and traces of corresponding eigenmodes. We use the adjoint method to calculate the shape derivative of this functional. The optimization is performed by BFGS, using a genetic algorithm as a preprocessor and the Method of Fundamental Solutions as a solver for the direct problem. We address several numerical simulations that illustrate the good performance of the method. Primary 74B05; Secondary 65N21,65N25, 65K10 inverse problem, shape optimization, eigenvalue problem, linear elasticity, adjoint method, method of fundamental solutions