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CCT-TR-2009-12
Title:
Variational Theory and Domain Decomposition for Nonlocal Problems
Authors:
Burak Aksoylu (corresponding author)
Michael L. Parks
Summary:
In this article we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincaré inequality and upper bound to establish a spectral equivalence. 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 single- and two-domain problems are presented.
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CCT-TR-2009-12.pdf
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