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 problems is, however, not well understood and has been an active area of research in recent years. The two most promising categories of unstructured multigrid methods are 1) \geometric" methods that use standard nite element coarse grid function spaces, and 2) rigid body mode based coarse grid space \algebraic" methods. This paper evaluates the e ectiveness of three promising multigrid methods (one geometric and two rigid body mode algebraic) on several unstructured problems in 3D elasticity with up to 76 million degrees of freedom.