Algebraic multigrid using inverse-based coarsening

In this talk we will review classical multigrid methods and give an overview on algebraic multigrid methods, in particular the "classical" approach to AMG by Ruge and Stueben.

After that we will introduce a new class of multilevel methods. These new AMGs on one hand and exploit information based on filtering vectors and on the other hand, information about the inverse matrix is used to drive the coarsening process.

This new kind of AMG will be discussed and compared with "classical" AMG from a theoretical point of view as well as by showing some numerical examples.