On the Algebraic Multigrid Method Based on Generic Approximate Banded Inverses

Abstract

Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago, significant progress has been made in improving and refining it. In this article, an AMG method is presented using generic approximate banded inverses based on incomplete LU factorization as smoothers. Finally, the applicability and effectiveness of the proposed AMG method on a characteristic two dimensional boundary value problem is demonstrated and numerical results on the convergence behavior and convergence factor are given.