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

A mathematical framework is provided for a substructuring-based domain decomposition (DD) approach nonlocal problems that features interactions between points separated by finite distance. Here, substructuring it meant traditional geometric configuration local partial differential equation (PDE) used in which computational subdivided into non-overlapping subdomains. In the setting, this sense those subdomains interact with neighboring domains over interface regions having volume, contrast to PDE setting interfaces are lower dimensional manifolds separating abutting Key results include equivalence global, single-domain problem and its multi-domain reformulation, both at continuous discrete levels. These provide rigorous foundation necessary development of efficient solution strategies DD methods.