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Defects play a critical role in the determination of mechanical properties of mechanical properties even at small concentrations. This is because defects couple the electronic structure of the core, the atomistic nature of the surrounding and the slow decay of elastic fields in an intimate and essential manner. This poses a challenge for modeling as one simultaneously needs the fidelity of density functional theory (DFT) as well as the long ranges of elastic fields. This talk describes an approach to doing so by solving the equations of density functional theory on very large domains of relevance to defects at physically realistic concentrations. It combines important ideas. The first  Linear Scaling Spectral Gauss Quadrature (LSSGQ)  reformulates density functional theory is such a manner that one can compute the electron density and electrostatic potential directly without having to resolve individual electronic orbitals. Importantly, these quantities can be computed at a spatial point with O(1) cost, thereby giving an O(N) algorithm. Second, we take advantage of the fact that the quantities of interest can be computed independently at each spatial point to adapt the spatial discretization so that we compute all the details in the core and but only sample far away. The resulting algorithm implemented in our MacroDFT code accurately solves the equations of density functional theory everywhere with no a priori ansatz or patches. The scaling is sublinear  O(N^1/2) or better  and enables simulations with computational domains of millions of atoms. The talk will give a background to DFT, introduce the reformulation and illustrate the method through selected examples.
Contact Turab Lookman at txl@lanl.gov to schedule time with Dr. Bhattacharya. 