Optimization–Based Coupling of Nonlocal and Local Diffusion Models. Issue 1753 (18th February 2015)

• Record Type: Journal Article
• Authors: D'Elia, Marta; Bochev, Pavel B.
• Editors: Calderer, C.; Lipton, R.; Margetis, D.; Otto, F.
• Is Part Of: MRS proceedings. Issue 1753:(2015)
• Publication Date: 2015-02-18
• Subjects: diffusion, -- microstructure, -- simulation; Electrical engineering -- Congresses; Physics -- Congresses; Materials -- Research -- Congresses; Materials science -- Congresses; 620.11
• DOI: 10.1557/opl.2015.109
• Languages: English
• ISSNs: 0272-9172

Abstract

ABSTRACT: In this work we introduce an optimization–based method for the coupling of nonlocal and local diffusion problems. Our approach is formulated as a control problem where the states are the solutions of the nonlocal and local equations, the controls are the nonlocal volume constraint and the local boundary condition, and the objective of the optimization is a matching functional for the state variables in the intersection of the nonlocal and local domains. For finite element discretizations we present numerical results in a one–dimensional setting; though preliminary, our tests show the consistency and efficacy of the method, and provide the basis for realistic simulations.