Analysis of Geometrically Consistent Schemes with Finite Range Interaction

DOI10.4208/cicp.OA-2017-0013zbMath1488.65636OpenAlexW2766891714MaRDI QIDQ5158996

Pingbing Ming, Hongliang Li

Publication date: 26 October 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/cicp.oa-2017-0013

zbMATH Keywords

stabilityquasicontinuum methodfinite range interactionsatomic-to-continuum coupling

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Cites Work

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• Cauchy-Born rule and the stability of crystalline solids: Static problems
• Energy-based atomistic-to-continuum coupling without ghost forces
• Justification of the Cauchy-Born approximation of elastodynamics
• An adaptive finite element approach to atomic-scale mechanics. -- The quasicontinuum method
• On the stability of Bravais lattices and their Cauchy–Born approximations
• A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction
• A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN
• Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions
• Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in Three Dimensions
• Stability Of A Force-Based Hybrid Method With Planar Sharp Interface
• An Optimization-based Atomistic-to-Continuum Coupling Method
• A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
• Analysis of Energy-Based Blended Quasi-Continuum Approximations
• Connecting Atomistic-to-Continuum Coupling and Domain Decomposition
• On Atomistic-to-Continuum Coupling by Blending
• An analysis of the effect of ghost force oscillation on quasicontinuum error
• Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method
• Convergence of a Force-Based Hybrid Method in Three Dimensions
• Construction and Sharp Consistency Estimates for Atomistic/Continuum Coupling Methods with General Interfaces: A Two-Dimensional Model Problem
• (In-)stability and Stabilization of QNL-Type Atomistic-to-Continuum Coupling Methods
• Atomistic-to-continuum coupling

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