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.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1631358
- Alternate ID(s):
- OSTI ID: 1237697; OSTI ID: 1373605
- Report Number(s):
- SAND-2015-7039J; S089812211500574X; PII: S089812211500574X
- Journal Information:
- Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 71 Journal Issue: 11; ISSN 0898-1221
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
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