Stability, instability, and error of the force-based quasicontinuum approximation

DOI10.1007/s00205-009-0276-zzbMath1268.74006arXiv0903.0610OpenAlexW3098399558MaRDI QIDQ993331

Christoph Ortner, Mitchell Luskin, Matthew Dobson

Publication date: 10 September 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.0610

zbMATH Keywords

coercivitylinearizationatomistic regioncontinuum region

Mathematics Subject Classification ID

Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Molecular, statistical, and kinetic theories in solid mechanics (74A25)

Related Items (28)

A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN ⋮ Linear Stationary Iterative Methods for the Force-Based Quasicontinuum Approximation ⋮ A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods ⋮ Analysis of blended atomistic/continuum hybrid methods ⋮ A field theoretical approach to the quasi-continuum method ⋮ A homogenization analysis of the field theoretic approach to the quasi-continuum method ⋮ Challenges in atomistic-to-continuum coupling ⋮ Energy-based atomistic-to-continuum coupling without ghost forces ⋮ Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice ⋮ Accuracy of quasicontinuum approximations near instabilities ⋮ Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems ⋮ Finite element analysis of Cauchy-Born approximations to atomistic models ⋮ A priori error analysis of two force-based atomistic/continuum models of a periodic chain ⋮ Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem ⋮ Convergence of a Force-Based Hybrid Method in Three Dimensions ⋮ Lattice Green function methods for atomistic/continuum coupling: theory and data-sparse implementation ⋮ Analysis of a Sinclair-Type Domain Decomposition Solver for Atomistic/Continuum Coupling ⋮ A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D ⋮ ELASTIC LIMIT OF SQUARE LATTICES WITH THREE-POINT INTERACTIONS ⋮ Blended Ghost Force Correction Method for 3D Crystalline Defects ⋮ An atomistic-based boundary element method for the reduction of molecular statics models ⋮ Analysis of a Predictor-Corrector Method for Computationally Efficient Modeling of Surface Effects in 1D ⋮ Atomistic/Continuum Blending with Ghost Force Correction ⋮ Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches ⋮ Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect ⋮ Theory-based benchmarking of the blended force-based quasicontinuum method ⋮ A Study on the Quasi-continuum Approximations of a One-Dimensional Fracture Model ⋮ An Atomistic/Continuum Coupling Method Using Enriched Bases

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