AMG by element agglomeration and constrained energy minimization interpolation

This paper studies AMG (algebraic multigrid) methods that utilize energy minimization construction of the interpolation matrices locally, in the setting of element agglomeration AMG. The coarsening in element agglomeration AMG is done by agglomerating fine‐grid elements, with coarse element matrices defined by a local Galerkin procedure applied to the matrix assembled from the individual fine‐grid element matrices. This local Galerkin procedure involves only the coarse basis restricted to the agglomerated element. To construct the coarse basis, one exploits previously proposed constraint energy minimization procedures now applied to the local matrix. The constraints are that a given set of vectors should be interpolated exactly, not only globally, but also locally on every agglomerated element. The paper provides algorithmic details, as well as a convergence result based on a ‘local‐to‐global’ energy bound of the resulting multiple‐vector fitting AMG interpolation mappings. A particular implementation of the method is illustrated with a set of numerical experiments. Copyright © 2006 John Wiley & Sons, Ltd.