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.