Speaker
Description
Algebraic multigrid methods are some of the most efficient methods used in the solution of large scale problems which often appear in engineering and physics theory and application. These methods rely entirely on the complementarity between a sequence of error relaxation processes each happening on a given scale within the hierarchy of scales present in the problem to be solved. The precise definition of true complementarity, although previously defined through numerical or heuristic arguments, is still illusive. In this talk, I will give a quick overview of a reformulation of the theory of algebraic multigrid through a novel coarse graining procedure applied to the relaxation process itself, one which allows us to better understand how multigrid operates and what true multiscale complementarity could look like.