abstract:
We will review some recent mathematical and numerical contributions related to nonperiodic multiscale problems. A typical setting is that of an elliptic equation with a highly oscillatory coefficient, modeling a structure with a set of embedded localized defects, or a structure that, although not periodic, enjoys nice geometrical features. The purpose is then to construct theoretical settings, and next numerical approaches providing an efficient and accurate approximation of the solution in several possible cases of practical interest.
This is joint work with Xavier Blanc (Paris 7), Pierre Louis Lions (College de France), Frederic Legoll (Ecole des Ponts) and several other collaborators. |