Aggregation-based algebraic multilevel preconditioning

摘要

We propose a preconditioning technique that is applicable in a "black box" fashion to linear systems arising from second order scalar elliptic PDEs discretized by finite differences or finite elements with nodal basis functions. This technique is based on an algebraic multilevel scheme with coarsening by aggregation. We introduce a new aggregation method which, for the targeted class of applications, produces semicoarsening effects whenever desirable, while the number of nodes is decreased by a factor of about 4 at each level, regardless of the problem at hand. Moreover, the number of nonzero entries per row in the successive coarse grid matrices remains approximately constant, ensuring small set up cost and modest memory requirements.