Algebraic multigrid methods for challenging large-scale geometrically complex problems

Speaker: Dr. Mark Adams, Sandia National Laboratory


Over the past few years algebraic multigrid (AMG) methods have begun to make an impact on challenging engineering and scientific applications. This talk discusses some of the speaker's contributions to this effort in terms of both mature production-quality software for applications with very complex geometry and the application of multigrid techniques to mathematically challenging (ie, not just Poisson-like) problems, such as Helmholtz operators and KKT systems, with strongly indefinite spectra.

The AMG solver package Prometheus is applied to large deformation finite element (FE) elasticity problems in micro-FE bone modeling with over a half a billion degrees of freedom. This work, with mechanical engineers at Berkeley, is a 2004 Gordon Bell prize finalist, uses the ASCI White machine at LLNL, achieves up to 0.47 sustained Teraflops on 4088 processors, and solves each linear system within an inexact Newton iteration in about a minute and a half. Time permitting, the application of Prometheus to a steel-rubber composite tire and an aircraft carrier will also be presented.

In the past few years, the speaker and his colleagues at Sandia have worked on the application of AMG techniques to mathematically challenging problems such as Maxwell's equations, constrained (Karush-Kuhn-Tucker) systems, and Helmholtz operators. A new framework for applying AMG techniques to linear systems with Lagrange multipliers (KKT systems) is presented, along with its application to contact problems in elasticity. Recent applications of AMG to complex-valued Helmholtz problems in elasticity will also be presented.

Last modified: Fri Jul 30 16:08:16 EDT 2004