4,762 research outputs found
Development of an Optimization-Based Atomistic-to-Continuum Coupling Method
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing
the properties of a discrete crystal structure, such as those containing
defects, that combine the accuracy of an atomistic (fully discrete) model with
the efficiency of a continuum model. In this note we extend the
optimization-based AtC, formulated in arXiv:1304.4976 for linear,
one-dimensional problems to multi-dimensional settings and arbitrary
interatomic potentials. We conjecture optimal error estimates for the
multidimensional AtC, outline an implementation procedure, and provide
numerical results to corroborate the conjecture for a 1D Lennard-Jones system
with next-nearest neighbor interactions.Comment: 12 pages, 3 figure
Formulation and optimization of the energy-based blended quasicontinuum method
We formulate an energy-based atomistic-to-continuum coupling method based on
blending the quasicontinuum method for the simulation of crystal defects. We
utilize theoretical results from Ortner and Van Koten (manuscript) to derive
optimal choices of approximation parameters (blending function and finite
element grid) for microcrack and di-vacancy test problems and confirm our
analytical predictions in numerical tests
Formulation and optimization of the energy-based blended quasicontinuum method
We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Van Koten and Luskin [32] and Ortner and Van Koten [24] to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests
Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions
Very few works exist to date on development of a consistent energy-based
coupling of atomistic and continuum models of materials in more than one
dimension. The difficulty in constructing such a coupling consists in defining
a coupled energy whose minimizers are free from uncontrollable errors on the
atomistic/continuum interface. In this paper a consistent coupling in three
dimensions is proposed. The main achievement of this work is to identify and
efficiently treat a modified Cauchy-Born continuum model which can be coupled
to the exact atomistic model. The convergence and stability of the method is
confirmed with numerical tests.Comment: 29 pages, 1 Matlab code. Typos corrected, exposition improve
Atomistic-to-continuum coupling approximation of a one-dimensional toy model for density functional theory
We consider an atomistic model defined through an interaction field satisfying a variational principle and which can therefore be considered a toy model of (orbital-free) density functional theory. We investigate atomistic-to-continuum coupling mechanisms for this atomistic model, paying special attention to the dependence of the atomistic subproblem on the atomistic region boundary and the boundary conditions. We rigorously prove first-order error estimates for two related coupling mechanisms
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