Related papers: Formulation, analysis and computation of an optimi…
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the…
In this paper, we extend the idea of "geometric reconstruction" to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial inconsistency,…
We propose a method to couple local and nonlocal diffusion models. By inheriting desirable properties such as patch tests, asymptotic compatibility and unintrusiveness from related splice and optimization-based coupling schemes, it enables…
We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with…
Local-to-Nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models…
In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the…
We demonstrate that nonlocal coupling enables control of the collective stochastic dynamics in the regime of coherence resonance. The control scheme based on the nonlocal interaction properties is presented by means of numerical simulation…
In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of…
We present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the coupling of the atomistic and continuum models as a constrained optimization problem with virtual Dirichlet controls on the…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. This paper studies the continuous and discrete formulations of three existing approaches for the…
This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…
In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing…
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the…
Achieving global optimality in nonlinear model predictive control (NMPC) is challenging due to the non-convex nature of the underlying optimization problem. Since commonly employed local optimization techniques depend on carefully chosen…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…
We consider a problem of optimal distribution of conductivities in a system governed by a non-local diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel…