Fast orthogonalization to the kernel of the discrete gradient operator with application to Stokes problem

Ivan Oseledets, Ekaterina Muravleva

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We obtain a simple tensor representation of the kernel of the discrete d-dimensional gradient operator defined on tensor semi-staggered grids. We show that the dimension of the nullspace grows as O (nd - 2), where d is the dimension of the problem, and n is one-dimensional grid size. The tensor structure allows fast orthogonalization to the kernel. The usefulness of such procedure is demonstrated on three-dimensional Stokes problem, discretized by finite differences on semi-staggered grids, and it is shown by numerical experiments that the new method outperforms usually used stabilization approach.

Original languageEnglish
Pages (from-to)1492-1500
Number of pages9
JournalLinear Algebra and Its Applications
Volume432
Issue number6
DOIs
Publication statusPublished - 1 Mar 2010
Externally publishedYes

Keywords

  • Discrete gradient operator
  • Fast orthogonalization
  • Kernel
  • Stokes problem
  • Tensor structure

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