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Summary: Evaluation of Three Unstructured Multigrid Methods on 3D Finite
Element Problems in Solid Mechanics
Mark Adams #
November 3, 2000
Abstract
Multigrid has been a popular solver method for finite element and finite 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 is easily available in most finite ele
ment applications (ie, 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) nonnested geometric multigrid, 2) smoothed ag
gregation 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.
Key words: unstructured multigrid, algebraic multigrid, parallel sparse solvers, finite element solvers
1 Introduction
The availability of large high performance computers is providing scientists and engineers with the oppor
tunity to simulate a variety of complex physical systems with ever more accuracy and thereby exploit the
advantages of computer simulations over laboratory experiments. The finite element method is widely used
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