A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions. (June 2016)

• Record Type: Journal Article
• Authors: D'Elia, Marta; Perego, Mauro; Bochev, Pavel; Littlewood, David
• Is Part Of: Computers & mathematics with applications. Volume 71:issue 11(2016)
• Page Start: 2218
• Page End: 2230
• Publication Date: 2016-06
• Subjects: Nonlocal models -- Coupling method -- Optimization -- Nonlocal vector calculus -- Mixed boundary conditions -- Nonlocal diffusion; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.12.006
• Languages: English
• ISSNs: 0898-1221

Abstract

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. 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.