Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory
Provides rigorous error analysis for multiscale coupling methods in materials science, though limited to a one-dimensional toy model.
The paper proves first-order error estimates for two atomistic-to-continuum coupling mechanisms in a toy model for density functional theory, addressing the dependence on boundary conditions.
We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functional theory. We investigate atomistic-to-continuum coupling mechanisms for this atomistic model, paying special attention to the dependence of the atomistic subproblem on the atomistic region boundary and the boundary conditions. We rigorously prove first-order error estimates for two related coupling mechanisms.