The Art of Molecular Dynamics Simulation
The Art of Molecular Dynamics Simulation
Numerical Methods for Engineers: With Software and Programming Applications
Numerical Methods for Engineers: With Software and Programming Applications
Partial Differential Equations: Analytical and Numerical Methods
Partial Differential Equations: Analytical and Numerical Methods
Coupling of atomistic and continuum simulations using a bridging scale decomposition
Journal of Computational Physics
A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations
Journal of Computational Physics
Journal of Computational Physics
Review: Meshless methods: A review and computer implementation aspects
Mathematics and Computers in Simulation
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As well known, one of the major challenges in developing a multiscale model is how to ensure a seamless interface between the constituent length/time scales. In order to overcome this challenge, a novel concurrent multiscale numerical method is proposed in this paper, which is based on the alternating Schwarz method, to provide the seamless coupling between the atomic and continuum scales. The novelty in this method is the use of the strong-form meshless Hermite---cloud method in the continuum domain for approximation of both the field variable and corresponding first-order derivative simultaneously. As a result, the coupling between the domains is achieved by ensuring the compatibility of both the field variable and the first-order derivative simultaneously across the overlapping transition region. The proposed scheme is validated numerically through both the static and transient benchmark case studies in 1- and 2-D domains. The numerical results show that the proposed method is simple, efficient, and accurate, and also provides a seamless coupling between the two domains.