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BIT Numerical Mathematics

, Volume 29, Issue 4, pp 748–768 | Cite as

Two-level hierarchically preconditioned conjugate gradient methods for solving linear elasticity finite element equations

  • M. Jung
  • U. Langer
  • U. Semmler
Preconditioned Conjugate Gradient Methods

Abstract

In this paper we study and compare some preconditioned conjugate gradient methods for solving large-scale higher-order finite element schemes approximating two- and three-dimensional linear elasticity boundary value problems. The preconditioners discussed in this paper are derived from hierarchical splitting of the finite element space first proposed by O. Axelsson and I. Gustafsson. We especially focus our attention to the implicit construction of preconditioning operators by means of some fixpoint iteration process including multigrid techniques. Many numerical experiments confirm the efficiency of these preconditioners in comparison with classical direct methods most frequently used in practice up to now.

AMS (MOS) Subject Classifications

65F10 65N20 

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Copyright information

© BIT Foundations 1989

Authors and Affiliations

  • M. Jung
    • 1
  • U. Langer
    • 1
  • U. Semmler
    • 1
  1. 1.Technical University of Karl-Marx-StadtGerman Democratic Republic

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