An efficient algebraic multigrid preconditioned conjugate gradient solver

Abstract

In this paper, we present a robust and efficient algebraic multigrid preconditioned conjugate gradient solver for systems of linear equations arising from the finite element discretization of a scalar elliptic partial differential equation of second order on unstructured meshes. The algebraic multigrid (AMG) method is one of most promising methods for solving large systems of linear equations arising from unstructured meshes. The conventional AMG method usually requires an expensive setup time, particularly for three dimensional problems so that generally it is not used for small and medium size systems or low-accuracy approximations. Our solver has a quick setup phase for the AMG method and a fast iteration cycle. These allow us to apply this solver for not only large systems but also small to medium systems of linear equations and also for systems requiring low-accuracy approximations.