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This content will become publicly available on December 21, 2016

Title: A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions

We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result, the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.
Authors:
 [1] ;  [1] ;  [1] ;  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
OSTI Identifier:
1237697
Report Number(s):
SAND--2015-7039J
Journal ID: ISSN 0898-1221; 601152
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 61; Journal Issue: C; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING nonlocal models; coupling method; optimization; nonlocal vector calculus; mixed boundary conditions; nonlocal diffusion