A new aggregation algorithm based on coordinates partitioning recursively for algebraic multigrid method

Abstract

Aggregation based algebraic multigrid is widely used to solve sparse linear systems, due to its potential to achieve asymptotic optimal convergence and cheap cost to set up. In this kind of method, it is vital to construct coarser grids based on aggregation. In this paper, we provide a new aggregation method based on coordinates partitioning recursively. The adjacent graph of the original coefficient matrix is partitioned into sub-graphs and each sub-graph is recursively partitioned until the minimal number of nodes over the sub-graphs on some level is small enough. In this way, a hierarchy of grids can be constructed from top to bottom, which is completely different from the classical schemes. The results from the solution of model partial differential equations with the preconditioned conjugate gradient iteration show that the new algorithm has better performance and is more robust than the widely used classical algorithms in most cases.