A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions

@article{Capodaglio2020AGF,
  title={A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions},
  author={Giacomo Capodaglio and Marta D'Elia and Max D. Gunzburger and Pavel B. Bochev and Manuel Klar and Christian Vollmann},
  journal={ArXiv},
  year={2020},
  volume={abs/2008.11780}
}
A rigorous mathematical framework is provided for a substructuring-based domaindecomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation problems is used in which a computational domain is subdivided into non-overlapping subdomains. In the nonlocal setting, this approach is substructuring-based in the sense that those… 

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