SC 99-22 Rudolf Beck: Graph-Based Algebraic Multigrid for Lagrange-Type Finite
Elements on Simplicial Meshes
Abstract: We present an algebraic multigrid preconditioner which
uses only the
graphs of system matrices. Some elementary coarsening
rules are stated,
from which an advancing front algorithm for the selection
of coarse grid
nodes is derived. This technique can be applied to linear
Lagrange-type
finite element discretizations; for higher-order elements
an extension of
the multigrid algorithm is provided. Both two- and
three-dimensional
second order elliptic problems can be handled. Numerical
experiments show
that the resulting convergence acceleration is comparable
to classical
geometric multigrid.
Keywords: Algebraic multigrid,
mesh coarsening,
preconditioning
MSC: 65-XX, 65N55, 65F10