Convergence of a Force-Based Hybrid Method in Three Dimensions
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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.
Published Version (Please cite this version)10.1002/cpa.21429
Publication InfoLu, Jianfeng; & Ming, P (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 http://hdl.handle.net/10161/14088.
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Associate Professor of Mathematics
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science and other related fields.More specifically, his current research focuses include:Electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis; rare events and sampling techniques.