 
Summary: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Numer. Linear Algebra Appl. 2000; 00:16 Prepared using nlaauth.cls [Version: 2002/09/18 v1.02]
Algebraic multigrid methods for constrained linear systems with
applications to contact problems in solid mechanics
Mark F. Adams1
1 Sandia National Laboratories, MS 9417, Livermore CA 94551 (mfadams@ca.sandia.gov)
SUMMARY
This paper develops a general framework for applying algebraic multigrid techniques to constrained
systems of linear algebraic equations that arise in applications with discretized PDEs. We discuss
constraint coarsening strategies for constructing multigrid coarse grid spaces and several classes of
multigrid smoothers for these systems. The potential of these methods is investigated with their
application to contact problems in solid mechanics. Copyright c 2000 John Wiley & Sons, Ltd.
key words: algebraic multigrid, multigrid methods, saddle point problems, parallel multigrid,
contact in solid mechanics
1. Introduction
This paper investigates the construction of algebraic multigrid methods for constrained linear
systemssaddle point problems or KKT systems. Discretized saddle point problems generate
systems of algebraic equations of the form:
Ax
K CT
