Comparison of two-level preconditioners derived from deflation, domain decomposition and multigrid methods

J. M. Tang, R. Nabben, C. Vuik, Y. A. Erlangga

Research output: Contribution to journalArticlepeer-review

69 Citations (Scopus)


For various applications, it is well-known that a multi-level, in particular two-level, preconditioned CG (PCG) method is an efficient method for solving large and sparse linear systems with a coefficient matrix that is symmetric positive definite. The corresponding two-level preconditioner combines traditional and projection-type preconditioners to get rid of the effect of both small and large eigenvalues of the coefficient matrix. In the literature, various two-level PCG methods are known, coming from the fields of deflation, domain decomposition and multigrid. Even though these two-level methods differ a lot in their specific components, it can be shown that from an abstract point of view they are closely related to each other. We investigate their equivalences, robustness, spectral and convergence properties, by accounting for their implementation, the effect of roundoff errors and their sensitivity to inexact coarse solves, severe termination criteria and perturbed starting vectors.

Original languageEnglish
Pages (from-to)340-370
Number of pages31
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - Jun 2009


  • Conjugate gradients
  • Deflation
  • Domain decomposition
  • Multigrid
  • SPD matrices
  • Two-grid schemes
  • Two-level PCG methods
  • Two-level preconditioning

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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