Non-nested and non-structured multigrid methods applied to elastic
                 problems. Part II: The three-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

Aspects of non-nested and non-structured multigrid methods with applications
to two-dimensional elastic problems were presented in a companion paper by the
current authors, Non-Nested and Non-Structured Multigrid Methods Applied to
Elastic Problems, Part I:  The Two-Dimensional Case.  In this paper a review
of some multigrid strategies, procedures for geometric search to implement
transfer operators, expressions for calculating the number of operations and
memory space, and aspects of convergence are presented.  Three-dimensional
elastic problems are solved by multigrid, sparse Gaussian elimination, and
conjugate gradient methods.  The number of operations and memory requirements
are compared.