Convergence of a Force-Based Hybrid Method in Three Dimensions
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2013-01-01
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We study a force-based hybrid method that couples an atomistic model with the Cauchy-Born elasticity model. We show that the proposed scheme converges to the solution of the atomistic model with second-order accuracy, since the ratio between lattice parameter and the characteristic length scale of the deformation tends to 0. Convergence is established for the three-dimensional system without defects, with general finite-range atomistic potential and simple lattice structure. The proof is based on consistency and stability analysis. General tools for stability analysis are developed in the framework opseudodifference operators in arbitrary dimensions. © 2012 Wiley Periodicals, Inc.
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Lu, J, and P Ming (2013). Convergence of a Force-Based Hybrid Method in Three Dimensions. Communications on Pure and Applied Mathematics, 66(1). pp. 83–108. 10.1002/cpa.21429 Retrieved from https://hdl.handle.net/10161/14088.
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Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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