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2011

Variational theory and domain decomposition for nonlocal problems

8 years 6 months ago
Variational theory and domain decomposition for nonlocal problems
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 Poincar´e 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.
Burak Aksoylu, Michael L. Parks
Added 12 May 2011
Updated 12 May 2011
Type Journal
Year 2011
Where AMC
Authors Burak Aksoylu, Michael L. Parks
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