A numerical exploration of algebraic multigrid
Jane Cullum
MS B256, CCS-3, Los Alamos National Laboratory,
Los Alamos, NM 87545, USA
Abstract
Algebraic multigrid (AMG) methods for
solving large systems of linear equations, Ax=b,
are matrix-based analogs of geometric
multigrid methods.
Both types of methods are multi-level,
with the method being applied recursively
at each level except at the bottom level.
In this talk we
focus on AMG procedures which are
based upon papers of Ruge and Stüben.
At each level, except the bottom level,
the procedure requires the choice of the
- Coarse and Fine variables
- Prolongation and Restriction operators
- Coarse problem
- Smoother operator
The choice of each of these components
places constraints upon the choice of each of
the other components.
Numerically, we explore the effects of
different choices upon the observed convergence.
We consider example problems where AMG
has been shown to work well and other example
problems where AMG converges
slowly.