Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics

Multigrid has been a popular solver method for finite element and finite difference problems with regular grids for over 20 years. The application of multigrid to unstructured grid problems, in which it is often difficult or impossible for the application to provide coarse grids, is not as well understood. In particular, methods that are designed to require only data that are easily available in most finite element applications (i.e. fine grid data), constructing the grid transfer operators and coarse grid operators internally, are of practical interest. We investigate three unstructured multigrid methods that show promise for challenging problems in 3D elasticity: (1) non-nested geometric multigrid, (2) smoothed aggregation, and (3) plain aggregation algebraic multigrid. This paper evaluates the effectiveness of these three methods on several unstructured grid problems in 3D elasticity with up to 76 million degrees of freedom. Published in 2002 by John Wiley Sons, Ltd.