Mathematics – Numerical Analysis
Scientific paper
2009-09-24
Mathematics
Numerical Analysis
Updated the technical part. In press in Applied Mathematics and Computation
Scientific paper
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.
Aksoylu Burak
Parks Michael L.
No associations
LandOfFree
Variational Theory and Domain Decomposition for Nonlocal Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Variational Theory and Domain Decomposition for Nonlocal Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Variational Theory and Domain Decomposition for Nonlocal Problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-425700