Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
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We prove aconvergence estimate for the Algebraic Multigrid Method with prolongations defined by aggregation using zero energy modes, followed by a smoothing. The method input is the problem matrix and a matrix of the zero energy modes. The estimate depends only polylogarithmically on the mesh size, and requires only a weak approximation property for the aggregates, which can be a-priori verified computationally. Construction of the prolongator in the case of a general second order system is described, and the assumptions of the theorem are verified for a scalar problem discretized by linear conforming finite elements.