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Quasi-Continuum Reduction of Field Theories: A Route to Seamlessly Bridge Quantum and Atomistic Length-Scales with Continuum

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Technical Report

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The Regents of the University of Michigan, Ann Arbor United States

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This report summarizes the research objectives achieved in this project during the period 03-01-2013 to 02-29-2016. Computational techniques have been developed that enable large-scale real-space electronic structure calculations using Kohn-Sham density functional theory. In particular, the various components of the developed techniques include i real-space formulation of Kohn-Sham density-functional theory DFT for both pseudopotential and all-electron calculations based on a finite-element discretization ii development of efficient and scalable algorithms for the solution of the Kohn-Sham eigenvalue problem based on Chebyshev filtering iii development of reduced order scaling techniques by employing a subspace projection technique in conjunction with localization techniques that construct a non-orthogonal localized basis spanning the Chebyshev filtered subspace iv leveraging the localized representation to construct the quasi-continuum reduction. Most aspects of these developments have been numerically implemented, and the benchmark studies have demonstrated that the developed techniques significantly outperform existing conventional DFT implementations in terms of computational efficiency, scaling with system size, and parallel scalability of the numerical implementation. We believe these developed techniques and the numerical implementation can aid as a platform for further development of scalable and efficient real-space Kohn-Sham DFT calculations on tens of thousands of atoms, and enable continuing efforts towards a seamless bridging of the quantum and continuum length-scales.

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