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

Journal Article · · Numerical Methods for Partial Differential Equations
DOI:https://doi.org/10.1002/num.22832· OSTI ID:1818992
 [1];  [2];  [3];  [4];  [5];  [5]
  1. Computational Physics and Methods Group Los Alamos National Laboratory Los Alamos New Mexico USA
  2. Computational Science and Analysis Sandia National Laboratories Livermore California USA
  3. Department of Scientific Computing Florida State University Tallahassee Florida USA
  4. Center for Computing Research Sandia National Laboratories Albuquerque New Mexico USA
  5. Department of Mathematics University of Trier Trier Germany
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Abstract

A mathematical framework is provided for a substructuring‐based domain decomposition (DD) approach for nonlocal problems that features interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation (PDE) 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 DD methods.

Sponsoring Organization:
USDOE
OSTI ID:
1818992
Alternate ID(s):
OSTI ID: 1996264
Journal Information:
Numerical Methods for Partial Differential Equations, Journal Name: Numerical Methods for Partial Differential Equations Journal Issue: 6 Vol. 38; ISSN 0749-159X
Publisher:
Wiley Blackwell (John Wiley & Sons)Copyright Statement
Country of Publication:
United States
Language:
English

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