Speaker
Description
This talk is concerned with inverse homogenisation problems that
aim to identify microstructure features of a body from macroscopic
measurements. The unknown microstructure is assumed to vary macroscopically and affects the effective tensor in an elliptic partial differential equation that governs the behaviour of the body on the macroscale. We establish the well-posedness of the PDE-constrained minimization problems that model the task of identifying the microstructure, derive first-order necessary optimality conditions,
and discuss a gradient-projection algorithm for the studied problem class in an infinite-dimensional setting. We moreover demonstrate that recently obtained results on generalized differentiability properties of
solution maps of bilateral obstacle problems make it possible to set up
and analyse a novel semismooth Newton method in the considered
situation. The latter outperforms classical approaches drastically and
opens up various directions for future research.