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Coarse-graining Kohn-Sham density functional theory. (English) Zbl 1258.81090

Summary: We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps. First, we develop a linear-scaling method that enables the direct evaluation of the electron density without the need to evaluate individual orbitals. We achieve this by performing Gauss quadrature over the spectrum of the linearized Hamiltonian operator appearing in each iteration of the self-consistent field method. Building on the linear-scaling method, we introduce a spatial approximation scheme resulting in a coarse-grained density functional theory. The spatial approximation is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. This coarse-graining step enables the analysis of defects at a fraction of the original computational cost, without any significant loss of accuracy. Furthermore, we show that the coarse-grained solutions are convergent with respect to the spatial approximation. We illustrate the scope, versatility, efficiency and accuracy of the scheme by means of selected examples.

MSC:

81V45 Atomic physics
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q31 Euler equations
82D25 Statistical mechanics of crystals
49S05 Variational principles of physics
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
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