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

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

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.


Contributed July 29, 1998.