Abstract

In this talk, I will review recent progress on fast solvers for the high-frequency Helmholtz equation. The problem is harder than in the elliptic case, and the better answers seem to involve a decomposition into polarized waves. I will describe how the method of polarized traces fits in this framework, and how it can be adapted to lead to a complexity that is sub-linear in both the number of volume unknowns and the number of right-hand sides, in the 3D case, in a parallel environment. Joint work with Laurent Demanet, Matthias Taus, Adrien Scheuer, and Leonardo Zepeda.