Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/7812
Title: Variational theory and domain decomposition for nonlocal problems
Authors: Aksoylu, Burak
Parks, Michael L.
Keywords: Domain decomposition
Nonlocal substructuring
Nonlocal operators
Nonlocal Poincare inequality
p-Laplacian
Peridynamics
Nonlocal Schur complement
Condition number
Issue Date: 2011
Publisher: Elsevier Science Inc
Abstract: In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a nonlocal Poincare inequality. To determine the conditioning of the discretized operator, we prove a spectral equivalence which leads to a mesh size independent upper bound for the condition number of the stiffness matrix. We then introduce a nonlocal two-domain variational formulation utilizing nonlocal transmission conditions, and prove equivalence with the single-domain formulation. A nonlocal Schur complement is introduced. We establish condition number bounds for the nonlocal stiffness and Schur complement matrices. Supporting numerical experiments demonstrating the conditioning of the nonlocal one- and two-domain problems are presented. (C) 2011 Elsevier Inc. All rights reserved.
URI: https://doi.org/10.1016/j.amc.2011.01.027
https://hdl.handle.net/20.500.11851/7812
ISSN: 0096-3003
1873-5649
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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