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Atomistic to continuum coupling approximation of a one dimensional toy model for density functional theory

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Figure

Fig. 2.1.and ρ Sketch of the basic atomistic problem: the field φ is periodic in Ω = (y−N−1, yN),y is a smooth particle density representing the atoms with positions given by y ∈ Y.
Fig. 3.1. The atomistic model in the domain Ωa with Dirichlet boundary conditions g = [gL gR]T.
Fig. 4.1.cells Q The Cauchy–Born approximation: independent periodic problems are solved on thej = (yj−1, yj) leading to locally defined fields ψ(j).
Fig. 5.1.is solved with the Dirichlet boundary conditionsis used in all cells An illustration of the first a/c method

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