Local multilevel preconditioners for elliptic equations with jump coefficients on bisection grids

Long Chen, Michael Holst, Jinchao Xu, Yunrong Zhu

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The goal of this paper is to design optimal multilevel solvers for the finite element approximation of second order linear elliptic problems with piecewise constant coefficients on bisection grids. Local multigrid and BPX preconditioners are constructed based on local smoothing only at the newest vertices and their immediate neighbors. The analysis of eigenvalue distributions for these local multilevel preconditioned systems shows that there are only a fixed number of eigenvalues which are deteriorated by the large jump. The remaining eigenvalues are bounded uniformly with respect to the coefficients and the meshsize. Therefore, the resulting preconditioned conjugate gradient algorithm will converge with an asymptotic rate independent of the coefficients and logarithmically with respect to the meshsize. As a result, the overall computational complexity is nearly optimal.

Original languageEnglish (US)
Pages (from-to)271-289
Number of pages19
JournalComputing and Visualization in Science
Volume15
Issue number5
DOIs
StatePublished - Oct 1 2012

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics

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