A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes

D. Cho, L. Zikatanov

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

This paper is on the efficient solution of linear systems arising in discretizations of second order elliptic PDEs by a generalized finite element method (GFEM). Our results apply for GFEM equations on unstructured simplicial grids in 2 and 3 spatial dimensions. We propose an efficient preconditioner by using auxiliary (fictitious) space techniques and an additive preconditioner for the auxiliary space problems. We also prove that the condition number of the preconditioned system is uniformly bounded with respect to the mesh parameters.

Original languageEnglish (US)
Pages (from-to)163-180
Number of pages18
JournalJournal of Numerical Mathematics
Volume15
Issue number3
DOIs
StatePublished - Oct 10 2007

All Science Journal Classification (ASJC) codes

  • Computational Mathematics

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