An optimal Schwarz preconditioner for a class of parallel adaptive finite elements

Sébastien Loisel, Hieu Nguyen

Research output: Contribution to journalArticle

3 Citations (Scopus)
25 Downloads (Pure)

Abstract

A Schwarz-type preconditioner is formulated for a class of parallel adaptive finite elements where the local meshes cover the whole domain. With this preconditioner, the convergence rate of the conjugate gradient method is shown to depend only on the ratio of the second largest and smallest eigenvalues of the preconditioned system. These eigenvalues can be bounded independently of the mesh sizes and the number of subdomains, which proves the proposed preconditioner is optimal. Numerical results are provided to support the theoretical findings.
Original languageEnglish
Pages (from-to)90–107
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume321
Early online date2 Mar 2017
DOIs
Publication statusPublished - Sep 2017

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