Related papers: Analysis of an optimization-based atomistic-to-con…
This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has been widely recognized that the most practical coupled…
We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling…
We propose a model-based, automated, bottom-up approach for design, which is applicable to various physical domains, but in this work we focus on the electrical domain. This bottom-up approach is based on a meta-topology in which each link…
We report a novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts. The continuum is treated in terms of quasi-atoms of…
We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For multi-body nearest-neighbour interactions on the 2D triangular lattice, we show that patch test…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
The atomistic-to-continuum (a/c) coupling methods, also known as the quasicontinuum (QC) methods, are a important class of concurrent multisacle methods for modeling and simulating materials with defects. The a/c methods aim to balance the…
In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…
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…
We study a force-based hybrid method that couples atomistic models with nonlinear Cauchy-Born elasticity models. We show that the proposed scheme converges quadratically to the solution of the atomistic model, as the ratio between lattice…
Peridynamics (PD) is widely used to simulate structural failure. However, PD models are time-consuming. To improve the computational efficiency, we developed an adaptive coupling model between PD and classical continuum mechanics (PD-CCM)…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
We present a multiscale atomistic-to-continuum method for ionic crystals with defects. Defects often play a central role in ionic and electronic solids, not only to limit reliability, but more importantly to enable the functionalities that…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
In this paper we construct energy based numerical methods free of ghost forces in three dimensional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite…
Inspired by the blending method developed by [P. Seleson, S. Beneddine, and S. Prudhome, \emph{A Force-Based Coupling Scheme for Peridynamics and Classical Elasticity}, (2013)] for the nonlocal-to-local coupling, we create a symmetric and…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
The simulation of geometrically resolved rigid particles in a fluid relies on coupling algorithms to transfer momentum both ways between the particles and the fluid. In this article, the fluid flow is modeled with a parallel Lattice…