Christina Frederic: Multiscale models for inverse homogenization

I will discuss inverse homogenization problems for elliptic partial differential equations with highly oscillating coefficients. The goal is to determine coefficients in the full equation using macroscopic properties of the solution. Such inverse problems pose a challenge in both the mathematical formulation and the numerical modeling, which is hard even for forward computations. In addition, the problem in its full generality is typically ill-posed; different sequences of coefficients produce the same limiting equations. I will discuss two mathematical aspects of this problem. One is determining conditions for the well-posedness of the inverse homogenization problem, and the second is the design of efficient computational meshes using tools from information theory. This is joint work with Björn Engquist.