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

Raúl A. Feijóo
Laboratório Nacional de Computação Científica (LNCC/CNPq)
Av. Getulio Vargas 333, CEP 25651-070, Petrópolis/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.


Contributed July 29, 1998.