Non-Galerkin multigrid based on sparsified smoothed aggregation

Eran Treister, Irad Yavneh

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Algebraic multigrid (AMG) methods are known to be efficient in solving linear systems arising from the discretization of partial differential equations and other related problems. These methods employ a hierarchy of representations of the problem on successively coarser meshes. The coarse-grid operators are usually defined by (Petrov-)Galerkin coarsening, which is a projection of the original operator using the restriction and prolongation transfer operators. Therefore, these transfer operators determine the sparsity pattern and operator complexity of the multigrid hierarchy. In many scenarios the multigrid operators tend to become much denser as the coarsening progresses. Such behavior is especially problematic in parallel AMG computations, where it imposes an expensive communication overhead. In this work we present a new algebraic technique for controlling the sparsity pattern of the operators in the AMG hierarchy, independently of the choice of the restriction and prolongation. Our method is based on the aggregation multigrid framework, and it "sparsifies" smoothed aggregation operators while preserving their right and left near null-spaces. Numerical experiments for problems of convection-diffusion and diffusion with discontinuous coefficients demonstrate the efficiency and potential of this approach.

Original languageEnglish
Pages (from-to)A30-A54
JournalSIAM Journal of Scientific Computing
Volume37
Issue number1
DOIs
StatePublished - 1 Jan 2015
Externally publishedYes

Keywords

  • Aggregation multigrid
  • Convection-diffusion
  • Matrix sparsification
  • Non-Galerkin multigrid
  • Parallel AMG
  • Smoothed aggregation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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