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

Multigrid has been a popular solver method for nite element and nite di erence problems with regular grids for over 20 years. The application of multigrid to unstructured grid problems, in which it is often di cult 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 nite element applications (i.e. ne 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 e ectiveness of these three methods on several unstructured grid problems in 3D elasticity with up to 76 million degrees of freedom