Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method

D'Elia, Marta; Bochev, Pavel Blagoveston

doi:10.1016/j.rinam.2020.100129

Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method

Journal Article · 22 October 2020 · Results in Applied Mathematics

DOI:https://doi.org/10.1016/j.rinam.2020.100129· OSTI ID:1429632

D'Elia, Marta ^[1]; Bochev, Pavel Blagoveston ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States). Computational Science and Analysis
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research

In this paper, we present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into 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 local and nonlocal problem domains, and the virtual controls are the nonlocal volume constraint and the local boundary condition. We present the method in the context of Local-to-Nonlocal di usion coupling. Numerical examples illustrate the theoretical properties of the approach.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1429632

Alternate ID(s):: OSTI ID: 1686215

Report Number(s):: SAND--2017-1029J; 650860

Journal Information:: Results in Applied Mathematics, Journal Name: Results in Applied Mathematics Journal Issue: C Vol. 9; ISSN 2590-0374

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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