A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions
Abstract
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:
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1631358
- Alternate Identifier(s):
- OSTI ID: 1237697; OSTI ID: 1373605
- Report Number(s):
- SAND-2015-7039J
Journal ID: ISSN 0898-1221; S089812211500574X; PII: S089812211500574X
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Published Article
- Journal Name:
- Computers and Mathematics with Applications (Oxford)
- Additional Journal Information:
- Journal Name: Computers and Mathematics with Applications (Oxford) Journal Volume: 71 Journal Issue: 11; Journal ID: ISSN 0898-1221
- Publisher:
- Elsevier
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; nonlocal models; coupling method; optimization; nonlocal vector calculus; mixed boundary conditions; nonlocal diffusion
Citation Formats
D’Elia, Marta, Perego, Mauro, Bochev, Pavel, and Littlewood, David. A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions. United Kingdom: N. p., 2016.
Web. doi:10.1016/j.camwa.2015.12.006.
D’Elia, Marta, Perego, Mauro, Bochev, Pavel, & Littlewood, David. A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions. United Kingdom. https://doi.org/10.1016/j.camwa.2015.12.006
D’Elia, Marta, Perego, Mauro, Bochev, Pavel, and Littlewood, David. Wed .
"A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions". United Kingdom. https://doi.org/10.1016/j.camwa.2015.12.006.
@article{osti_1631358,
title = {A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions},
author = {D’Elia, Marta and Perego, Mauro and Bochev, Pavel and Littlewood, David},
abstractNote = {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.},
doi = {10.1016/j.camwa.2015.12.006},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 11,
volume = 71,
place = {United Kingdom},
year = {Wed Jun 01 00:00:00 EDT 2016},
month = {Wed Jun 01 00:00:00 EDT 2016}
}
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https://doi.org/10.1016/j.camwa.2015.12.006
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