Non-nested and non-structured multigrid methods applied to elastic
                  problems. Part I: The two-dimensional case

                             Marco L. Bittencourt
                      Center for Computational Sciences
                            University of Kentucky
               325 McVey Hall, Lexington, KY, 40506-0045, USA 
                           e-mail: mlb@ccs.uky.edu

                               Craig C. Douglas
                          Department of Mathematics
                            University of Kentucky
          715 Patterson Office Tower, Lexington, KY, 40506-0027, USA
                         e-mail: douglas@ccs.uky.edu

                                Raul A. Feijoo
          Laboratorio Nacional de Computacao Cientifica (LNCC/CNPq)
        Av. Getulio Vargas 333, CEP 25651-070, Petropolis/RJ, Brazil 
                          e-mail: feij@alpha.lncc.br

                                   Abstract

This paper presents the application of non-nested and non-structured multigrid
methods for two-dimensional elastic linear problems.  Some basic aspects
related to multigrid methods are discussed including nested iterations, coarse
grid correction scheme, transfer operators, and multigrid strategies.  A
variational formulation for the transfer operators is also considered.  The
C++ implementation of the multigrid software is discussed and some examples
are analyzed.  The performance of multigrid strategies is compared with direct
and pre-conditioned conjugate gradient algorithms.