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An atomistic/continuum coupling method using enriched bases. (English) Zbl 1317.65224

Summary: A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to suppress the error at the interface, and as a consequence, the overall accuracy is improved. The method is motivated by formulating the molecular mechanics model as a two-stage minimization problem. In particular, it is demonstrated that the error at the interface can be considerably reduced when new basis functions are introduced in a Galerkin projection formalism. The improvement of the accuracy is illustrated by two examples. Further, comparison with some quasi-continuum-type methods is provided.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
70E55 Dynamics of multibody systems
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