Effective Approximation for PDE with Highly Oscillatory Coefficient
Please login to view abstract download link
This presentation deals with inverse problems in a the context of multiscale PDEs. For a given multiscale problem, we propose to reconstruct some characteristic quantities associated to the PDE, based on the knowledge of its solutions. Typically, these quantities are inspired by homogenization theory (e.g. effective coefficient, corrector). The goal is to develop a numerical methodology that can handle cases beyond those traditionally considered by the homogenization theory (which have to satisfy assumptions that can be restrictive in practice (e.g. periodicity)), and that can be valid even outside the specific case where scales are well separated.
