A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions [including apppendix B]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
- Florida State Univ., Tallahassee, FL (United States)
- Univ. Trier (Germany)
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition 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 subdomains interact with neighboring domains over interface regions having finite volume, in contrast to the local PDE setting in which interfaces are lower dimensional manifolds separating abutting subdomains Key results include the equivalence between the global, single-domain nonlocal problem and its multi-domain reformulation, both at the continuous and discrete levels. These results provide the rigorous foundation necessary for the development of efficient solution strategies for nonlocal domain-decomposition methods.
- Research Organization:
- Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1656937
- Report Number(s):
- SAND--2020-8734R; 690103
- Country of Publication:
- United States
- Language:
- English
Similar Records
A general framework for substructuringâbased domain decomposition methods for models having nonlocal interactions