Petr Vanek*, Jan Mandel, and Marian Brezina
Center for Computational Mathematics
University of Colorado at Denver
Denver CO 80217-3364

An algebraic multigrid algorithm for symmetric, positive definite
linear systems is developed based on the concept of prolongation by
smoothed aggregation. Coarse levels are generated automatically.
We present a set of requirements motivated heuristically by a convergence
theory.  The algorithm then attempts to satisfy the requirements.
Input to the method are the coefficient matrix and zero energy modes,
which are determined from nodal coordinates and knowledge of the
differential equation.
Efficiency of the resulting algorithm is demonstrated by
computational results on real world problems from solid elasticity,
plate bending, and shells.