Numerical Linear Algebra With Applications vol:13 issue:2-3 pages:105-131
This paper is concerned with algebraic multigrid for finite element discretizations of the divgrad, curlcurl and graddiv equations on tetrahedral meshes with piecewise linear shape functions. First, an edge, face and volume prolongator are derived from an arbitrary partition of unity nodal prolongator for a tetrahedral fine mesh, using the formulas for edge, face and volume elements. This procedure can be repeated recursively. The implied coarse topology and the normalization of the prolongators are analysed. It is proved that the range spaces of the nodal prolongator and of the derived edge, face and volume prolongators form a discrete de Rham complex if these prolongators have full rank. It is shown that on simplicial meshes, the constructed edge prolongator is a generalization of the Reitzinger-Schoberl prolongator. The derived edge and face prolongators are applied in an algebraic multigrid method for the curlcurl and graddiv equations, and numerical results are presented. Copyright (c) 2006 John Wiley & Sons. Ltd.