ALEX 2018 Workshop: Abstracts

Multipole expansion in random media

Felix Otto

Max Planck Institute for Mathematics in the Sciences Leipzig (Germany)

In a homogeneous medium, the far-field generated by a local source is well-described by the multipole expansion, the coefficients of which are given by the moments of the charge distribution. In case of a random medium that homogenizes, this is not covered by standard homogenization theory, since the source lives on a scale comparable to the correlation length. However, the constant-coefficient situation survives, intrinsically interpreted, to some degree: In three space dimensions, the analogy holds up to quadrupoles. This insight allows, for instance, to identify the best artificial boundary conditions for a finite computational domain.

This is joint work with P. Bella & A. Giunti, and with JF. Liu, based on work with J. Fischer.