Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session H36: RealSpace Methods for Large Scale Electronic Structure ProblemsInvited

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Sponsoring Units: DCOMP Chair: Leeor Kronik, Weizmann Institute of Science Room: BCEC 205C 
Tuesday, March 5, 2019 2:30PM  3:06PM 
H36.00001: Realspace numerical grid methods: The next generation of electronic structure codes Invited Speaker: James Chelikowsky Two physical ingredients, pseudopotentials and density functional theory, are widely used in electronic structure computations for a variety of materials applications. If we wish to address large, complex systems, the implementation of these ingredients on high performance computational platforms is vital. Real space grid methods offer a compelling vehicle for such computations. These methods are mathematically robust, very accurate and well suited for modern, massively parallel computing resources [1]. I will illustrate the utility of these methods as implemented in the PARSEC code [2]. Key algorithms in this code include subspace filtering based on Chebyshev polynomials for an accelerated eigenvalue solution, spectrum slicing for an added level of parallelism, Cholesky QR algorithms to improve the performance of orthogonalization, and a 2D partition of the wave functions for efficient matrixvector operations. Applications will be illustrated for nanostructures containing tens of thousands of atoms. 
Tuesday, March 5, 2019 3:06PM  3:42PM 
H36.00002: Largescale densityfunctional calculations in real space and its application to bilayer graphene and semiconductor epitaxial growth Invited Speaker: Atsushi Oshiyama Facing current and future massively parallel architecture of supercomputers, we need to make close collaboration between the fields of physical science and computer science. Such collaboration we name COMPUTICS is already in progress (http://computicsmaterial.jp/indexe.html). I here explain an example of such collaboration which allows us to perform totalenergy electronicstructure calculations based on the densityfunctional theory (DFT) in the realspace scheme for tensofthousandsatom systems and also the realspace CarParrinello Molecular Dynamics simulations for thousandsofatom systems. I first explain how we are able to perform such largescale computations efficiently in our code named RSDFT. Recent development of the device simulation combined with the nonequilibrium Green’s function (NEGF) method and its application to Si nanowire MOSFETs are also reported. As examples of the application to materials science, I will discuss (1) the localization of Dirac electrons induced by moire pattern in twisted bilayer graphene, (2) ammonia decomposition and N incorporation on epitaxially grown GaN films, (3) intrinsic carrier traps near SiC/SiO2 interfaces, and possibly (4) the formation of amorphous systems with thousands of atoms. 
Tuesday, March 5, 2019 3:42PM  4:18PM 
H36.00003: Discontinuous projection method for large, accurate electronic structure calculations in real space Invited Speaker: John Pask For decades, the planewave (PW) pseudopotential method has been the method of choice for large, accurate KohnSham calculations of condensed matter systems, in ab initio molecular dynamics simulations in particular. However, due to its reliance on a Fourier basis, the method has proven notoriously difficult to parallelize at scale, thus limiting the length and time scales accessible. In this talk, we discuss new developments aimed at increasing the scales accessible substantially, while retaining the fundamental simplicity, systematic convergence, and generality instrumental to the PW method's success in practice. The key idea is to release the constraint of continuity in the basis set, and with the freedom so obtained, employ a basis of local KohnSham eigenfunctions to solve the global KohnSham problem. In so doing, the basis obtained is highly efficient, requiring just a few tens of basis functions per atom to attain chemical accuracy, while simultaneously strictly local, orthonormal, and systematically improvable. We show how this basis can be employed to accelerate current stateoftheart realspace methods substantially by reducing the dimension of the realspace Hamiltonian by up to three orders of magnitude. Results for metallic and insulating systems of up to 27,000 atoms using up to 38,000 processors demonstrate the scalability of the methodology in a discontinuous Galerkin formulation. Proceeding via projection of the realspace Hamiltonian instead promises to reach larger scales still. 
Tuesday, March 5, 2019 4:18PM  4:54PM 
H36.00004: Efficient Computation of Hybrid and Screened Hybrid Functionals in RealSpace with Projection Operators Invited Speaker: Amir Natan The use of hybrid and screened hybrid functionals in Density Functional Theory (DFT) became popular as they allow to reduce the error between the calculated and experimentally measured properties. The calculation of the Fock exchange operator, required for those methods, is becoming a computationally prohibitive task with system size. An efficient approach, is to replace the explicit calculation of the Fock operator with its projection on the Hilbert subspace that is spanned by the previous selfconsistent field (SCF) occupied eigenvectors. It is possible to extend the method by projecting also on low lying empty eigenvectors to calculate also the empty eigenvalues. We have implemented this method^{1} within the PARSEC^{2,3} realspace code and combined it with efficient Poisson solvers^{4} and further hardware acceleration by Graphical Processing Units (GPUs) to achieve affordable hybrid calculations of atomistic structures with 1000 atoms on a single workstation^{5}. We demonstrate the efficiency of this method by calculating the electronic properties of silicon quantum dots (QD) and graphene nanoribbons with hybrid and screened hybrid functionals (e.g. PBE0 and HSE)^{5}. We show how the formalism can be equally applied in realspace to 3D^{6} and 2D periodic systems. 
Tuesday, March 5, 2019 4:54PM  5:30PM 
H36.00005: Computational Materials Discovery by RESCU  a KSDFT method for solving thousands of atoms Invited Speaker: Hong Guo A major bottleneck for solving realistic materials problems is the lack of a first principles method that can accurately, efficiently and comfortably calculate condensed phase materials comprising thousands of atoms. Solving large systems is necessary when dealing with structures involving interfaces, surfaces, dilute impurities, grain boundaries, dislocations, domains, solvents etc. Wellknown methods of Kohn–Sham density functional theory (KSDFT) can solve problems at a few hundred atoms level on a modest computer. For larger systems, supercomputers or further approximations are necessary. Here I shall present our effort in developing a generalpurpose KSDFT solver called RESCU (stand for real space electronic structure calculator). We demonstrate that RESCU can easily compute electronic structure for systems comprising thousands of atoms on a modest computer, for metals, semiconductors, insulators, liquids, moire patterns in 2D heterjunction materials, dilute doped IIInitrides etc. For these problems and up to 14,000 atoms as we have used it for, RESCU converges KSDFT in a few to ten wallclock hours. RESCU achieves high efficiency without compromising accuracy. I shall present the novel computational mathematics behind the efficiency gain^{1}, and apply it for property discovery of materials. 
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