Spectral finite-element based methodology for large scale-electronic structure calculations using Kohn-Sham density functional theory
Phani Motamarri (University of Michigan Ann Arb), Vikram Gavini (University of MIchigan)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A
Tue 4:20 - 5:40
CIT 165
Material defects, though occur in very small concentrations, influence many macroscopic properties of materials. The development of a mathematical model which accurately describes such defects presents a unique challenge since such a model must incorporate physics spanning multiple length scales. One of the most popular electronic structure theories which can be used to achieve the above goal is Kohn-Sham density functional theory (DFT). However, the complexity of these calculations restricts the computations to sample sizes of the order of a few hundred atoms. To extend the DFT calculations to realistic sample sizes that can accurately capture the long ranged fields generated by defects, an efficient approach that can seamlessly bridge quantum mechanical and continuum scales using ‘single physics’ (DFT) is highly desirable. As a first step towards developing a multi-scale method with DFT, we develop an efficient approach to perform electronic structure calculations using an adaptive higher-order spectral finite-element discretization of DFT. The key ideas involved are to use an a-priori mesh adaption technique and subsequently employ Chebyshev acceleration strategies in conjunction with special quadrature rules to reduce the computational cost in solving the DFT problem. Next,we address the problem of computational complexity involved in solving the DFT problem which scales cubically with number of atoms in the system. This is a significant bottleneck since the development of a multi-scale approach requires few thousands of atoms to capture relevant physics. To this end, we formulate a linear-scaling algorithm, within the framework of spectral finite-elements. The proposed linear-scaling approach allows for the treatment of both metallic and insulating systems on the same footing. We further demonstrate the efficacy of the proposed algorithm on some representative benchmark examples.