New interpolation formulas of using geometric assumptions in the algebraic multigrid method

摘要

In this paper, new interpolation formulas for using geometric assumptions in the algebraic multigrid (AMG) method are reported. The theoretical and convergence analysis will be presented. The effectiveness and robustness of these interpolation formulas are demonstrated by numerical experiments. Not only is a rapid rate of convergence achieved, but the AMG algorithm used in conjunction with these formulas can also be used to solve various ill-conditioned systems of equations. The principal contribution of the present method is to extend the range of applications of the AMG method developed by Ruge and Stüben.