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COMMUN. MATH. SCI. c 2007 International Press Vol. 5, No. 4, pp. 9991026
 

Summary: COMMUN. MATH. SCI. c 2007 International Press
Vol. 5, No. 4, pp. 999­1026
A SUB-LINEAR SCALING ALGORITHM FOR COMPUTING THE
ELECTRONIC STRUCTURE OF MATERIALS
CARLOS J. GARC´IA-CERVERA, JIANFENG LU, AND WEINAN E§
Abstract. We introduce a class of sub-linear scaling algorithms for analyzing the electronic
structure of crystalline solids with isolated defects. We divide the localized orbitals of the electrons
into two sets: one set associated with the atoms in the region where the deformation of the material
is smooth (smooth region), and the other set associated with the atoms around the defects (non-
smooth region). The orbitals associated with atoms in the smooth region can be approximated
accurately using asymptotic analysis. The results can then be used in the original formulation to
find the orbitals in the non-smooth region. For orbital-free density functional theory, one can simply
partition the electron density into a sum of the density in the smooth region and a density in the
non-smooth region. This kind of partition is not used for Kohn-Sham density functional theory and
one uses instead the partition of the set of orbitals. As a byproduct, we develop the necessary real
space formulations and we present a formulation of the electronic structure problem for a subsystem,
when the electronic structure for the remaining part is known.
Key words. sub-linear scaling algorithms, asymptotics, DFT-continuum approximation, density
functional theory
AMS subject classifications. 35Q40, 74Q05, 34E05

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics