Subspace correction multi-level methods for elliptic eigenvalue problems

Tony Chan, Ilya Sharapov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In this work, we apply the ideas of domain decomposition and multi-grid methods to PDE-based eigenvalue problems represented in two equivalent variational formulations. To find the lowest eigenpair, we use a "subspace correction" framework for deriving the multiplicative algorithm for minimizing the Rayleigh quotient of the current iteration. By considering an equivalent minimization formulation proposed by Mathew and Reddy, we can use the theory of multiplicative Schwarz algorithms for nonlinear optimization developed by Tai and Espedal to analyse the convergence properties of the proposed algorithm. We discuss the application of the multiplicative algorithm to the problem of simultaneous computation of several eigenfunctions also formulated in a variational form. Numerical results are presented.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalNumerical Linear Algebra with Applications
Volume9
Issue number1
DOIs
StatePublished - Jan 1 2002

Keywords

  • Domain decomposition
  • Eigenvalues
  • Multigrid

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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