Algebraic multigrid (AMG): experiences and comparisons

摘要

Algebraic multigrid methods are designed for the solution of (sparse) linear systems of equations using multigrid principles. In contrast to standard multigrid methods, AMG does not take advantage of the origin of a particular system of equations at hand, nor does it exploit any underlying geometrical situation. Fully automatically and based solely on algebraic information contained in the given matrix, AMG constructs a sequence of “grids” and corresponding operators. A special AMG algorithm will be presented. For a wide range of problems (including certain problems which do not have a continuous background) this algorithm yields an iterative method which exhibits a convergence behavior typical for multigrid methods.