相关论文: There is no pointwise consistent quasicontinuum en…
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the…
We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods. Our results are valid in two and three dimensions, for…
Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are an exciting development in computational physics. For example, the force-based quasicontinuum approximation is the only known pointwise…
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy…
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around…
We consider the energy norm arising from elliptic problems with discontinuous piecewise constant diffusion. We prove that under the quasi-monotonicity property on the diffusion coefficient, the best approximation error with continuous…
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…
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…
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…
Extrapolating the coupling strengths to very high energies, one finds that they do not converge to a single coupling constant, as expected in the simplest gauge theory of Grand Unification, the SU(5) theory. We find that the coupling…
The development of patch test consistent quasicontinuum energies for multi-dimensional crystalline solids modeled by many-body potentials remains a challenge. The original quasicontinuum energy (QCE) has been implemented for many-body…
Ensemble inequivalence has been previously displayed only for long-range interacting systems with non-extensive energy. In order to perform the thermodynamic limit, such systems require an unphysical, so-called, Kac rescaling of the…
We formulate a patch test consistent atomistic-to-continuum coupling (a/c) scheme that employs a second-order (potentially higher-order) finite element method in the material bulk. We prove a sharp error estimate in the energy-norm, which…
The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries, occurs when the lattice configuration loses stability, that is, when an eigenvalue of the Hessian of the lattice energy functional becomes…
Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…
We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual…
We present a posteriori error estimates for a recently developed atomistic/continuum coupling method, the Consistent Energy-Based QC Coupling method. The error estimate of the deformation gradient combines a residual estimate and an a…
It is well known in quantum mechanics that a large energy gap between a Hilbert subspace of specific interest and the remainder of the spectrum can suppress transitions from the quantum states inside the subspace to those outside due to…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
We show that quasiparticle (QP) energies as calculated in the $GW$ approximation converge to the wrong value using the projector augmented wave (PAW) method, since the overlap integrals between occupied orbitals and high energy, plane wave…