CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
UNIVERSITY OF COLORADO AT DENVER
TITLE: Algebraic Multigrid Methods for Structural Problems
SPEAKER: John Ruge, Department of Mathematics, UCD
DATE: Wednesday, November 29, 1995
PLACE: Math Conference Room - Suite 540
UCD Building, 1250 14th St., Denver
TIME: 2:30 pm (Refreshments served at 2:15 pm)
ABSTRACT:
Algebraic multigrid (AMG) is a method for solving a given matrix
problem using multigrid principles. The coarser levels and grid
transfer operators are determined automatically, and a standard
multigrid cycling scheme is then used for the solution process.
AMG is not a true "black-box" solver, but algorithms can be
developed for classes of problems. Within these classes, AMG is
very robust with respect to varying or discontinuous problem
coefficients, irregular domains, and irregular or unstructured
meshes. This talk introduces the basic AMG method, which developed
to apply to discretized second order elliptic PDE's, and then
covers our work in extending the method to problems in elasticity.
The main problem is in choosing the coarser grids and interpolation
weights so that the smoothest error components (those with the
least energy) can be accurately represented on the coarser levels,
which is critical for optimal convergence. We introduce a method
we developed that we call "element interpolation" and present
results for model problems (both elasticity and discrete structures)
showing typical MG convergence behavior.