Robustness and scalability of algebraic multigrid

Algebraic multigrid (AMG) is currently undergoing a resurgence in popularit y, due in part to the dramatic increase in the need to solve physical probl ems posed on very large, unstructured grids. While AMG has proved its usefu lness on various problem types, it is not commonly understood how wide a ra nge of applicability the method has. In this study, we demonstrate that ran ge of applicability, while describing some of the recent advances in AMG te chnology. Moreover, in light of the imperatives of modern computer environm ents, 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 in dicate the current directions taken by AMG researchers to alleviate these d ifficulties.