Elsevier

Journal of Sound and Vibration

Volume 20, Issue 3, 8 February 1972, Pages 333-342
Journal of Sound and Vibration

Optimal gradient minimization scheme for finite element eigenproblems

https://doi.org/10.1016/0022-460X(72)90614-1Get rights and content

Abstract

A gradient minimization technique is developed for the solution of the general algebraic eigenproblem Kx = λMx arising from the application of the finite element method. The essence of the technique consists of a simultaneous linear and directional searches so as to obtain the highest rate of convergence.

The effect of round-off errors on the obtainable accuracy in the eigenvalues and eigenvectors is established as a function of the properties of K and M.

An a-posteriori error estimate and a practical termination criterion are also given in the paper.

References (16)

There are more references available in the full text version of this article.

Cited by (32)

  • Solving the Bethe-Salpeter equation on massively parallel architectures

    2021, Computer Physics Communications
    Citation Excerpt :

    The advantage of subspace methods is that the search space for the eigenvectors can be treated as one contiguous block and further refined at each iteration of the eigensolver. This is the main philosophy behind the version of the Conjugate Gradient (CG) method [18,19] modified by Kalkreuter and Simma (KSCG) in their work [41]. Originally conceived for applications in Quantum Chromodynamics, the KSCG eigensolver parallel implementation is based on geometrical data decomposition where vectors are equally partitioned and stored on distinct processing nodes.

  • Gradient eigenanalysis on nested finite elements

    1996, Advances in Engineering Software
  • A new simulation algorithm for lattice QCD with dynamical quarks

    1995, Nuclear Physics B (Proceedings Supplements)
View all citing articles on Scopus
View full text