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• W2952976008 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." @default.
• W2952976008 created "2019-06-27" @default.
• W2952976008 creator A5045341706 @default.
• W2952976008 creator A5078880740 @default.
• W2952976008 date "2009-09-24" @default.
• W2952976008 modified "2023-09-23" @default.
• W2952976008 title "Variational Theory and Domain Decomposition for Nonlocal Problems" @default.
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• W2952976008 hasPublicationYear "2009" @default.
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