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.