LDRD Final Report. New Directions for Algebraic Multigrid: Solutions for Large Scale Multiphysics Problems

摘要

The purpose of this research project was to investigate, design, and implement new algebraic multigrid (AMG) algorithms to enable the effective use of AMG in large-scale multiphysics simulation codes. These problems are extremely large; storage requirements and excessive run-time make direct solvers infeasible. The problems are highly ill-conditioned, so that existing iterative solvers either fail or converge very slowly. While existing AMG algorithms have been shown to be robust and stable for a large class of problems, there are certain problems of great interest to the Laboratory for which no effective algorithm existed prior to this research.