Related papers: Formulation, analysis and computation of an optimi…
Nonlocal interaction is shown to be an appropriate tool for controlling coherence resonance in ensembles of non-excitable oscillators. The constructive role of nonlocal coupling is demonstrated through numerical simulations on an example of…
Local-nonlocal coupling approaches combine the computational efficiency of local models and the accuracy of nonlocal models. However, the coupling process is challenging, requiring expertise to identify the interface between local and…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-based atomistic model, which enables accurate simulation of the…
The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…
Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and…
Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if…
In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua…
The analysis of an optimal control problem of nonlocal type is analyzed. The results obtained are applied to the study the corresponding local optimal control problems. The state equations are governed by p-laplacian elliptic operators, of…
In this work we study a general shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze…
We introduce two different ways of coupling local and nonlocal equations with Neumann boundary conditions in such a way that the resulting model is naturally associated with an energy functional. For these two models we prove that there is…
The Global-Local non-invasive coupling is an improvement of the submodeling technique, which permits to locally enhance structure computations by introducing patches with refined models and to take into accounts all the interactions. In…
In this paper we design and analyze an explicit partitioned procedure for a 2D dynamic local-to-nonlocal (LtN) coupling problem, based on a new nonlocal Robin-type transmission condition. The nonlocal subproblem is modeled by the nonlocal…
In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connection, we hope to promote the cross fertilization of ideas…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
In this article we study a non-local diffusion problem that involves three different fractional Laplacian operators acting on two domains. Each domain has an associated operator that governs the diffusion on it, and the third operator…
We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the…
Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the…
Diffusion models have exhibited impressive prowess in the text-to-image task. Recent methods add image-level structure controls, e.g., edge and depth maps, to manipulate the generation process together with text prompts to obtain desired…
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying…