Robustness and Scalability of Algebraic Multigrid

Algebraic multigrid (AMG) is currently undergoing a resurgence in popularity, due in part to the dramatic increase in the need to solve physical problems posed on very large, unstructured grids. While AMG has proved its usefulness on various problem types, it is not commonly understood how wide a range of applicability the method has. In this study, we demonstrate that range of applicability, while describing some of the recent advances in AMG technology. Moreover, in light of the imperatives of modern computer environments, we also examine AMG in terms of algorithmic scalability. Finally, we show some of the situations in which standard AMG does not work well and indicate the current directions taken by AMG researchers to alleviate these difficulties.