Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session H36: Real-Space 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: Real-space 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 matrix-vector operations. Applications will be illustrated for nanostructures containing tens of thousands of atoms. |
Tuesday, March 5, 2019 3:06PM - 3:42PM |
H36.00002: Large-scale density-functional 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://computics-material.jp/index-e.html). I here explain an example of such collaboration which allows us to perform total-energy electronic-structure calculations based on the density-functional theory (DFT) in the real-space scheme for tens-of-thousands-atom systems and also the real-space Car-Parrinello Molecular Dynamics simulations for thousands-of-atom systems. I first explain how we are able to perform such large-scale computations efficiently in our code named RSDFT. Recent development of the device simulation combined with the non-equilibrium 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 Kohn-Sham 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 Kohn-Sham eigenfunctions to solve the global Kohn-Sham 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 state-of-the-art real-space methods substantially by reducing the dimension of the real-space 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 real-space 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 Real-Space 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 sub-space that is spanned by the previous self-consistent 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 method1 within the PARSEC2,3 real-space code and combined it with efficient Poisson solvers4 and further hardware acceleration by Graphical Processing Units (GPUs) to achieve affordable hybrid calculations of atomistic structures with 1000 atoms on a single workstation5. We demonstrate the efficiency of this method by calculating the electronic properties of silicon quantum dots (QD) and graphene nano-ribbons with hybrid and screened hybrid functionals (e.g. PBE0 and HSE)5. We show how the formalism can be equally applied in real-space to 3D6 and 2D periodic systems. |
Tuesday, March 5, 2019 4:54PM - 5:30PM |
H36.00005: Computational Materials Discovery by RESCU - a KS-DFT 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. Well-known methods of Kohn–Sham density functional theory (KS-DFT) 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 general-purpose KS-DFT 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 III-nitrides etc. For these problems and up to 14,000 atoms as we have used it for, RESCU converges KS-DFT in a few to ten wall-clock hours. RESCU achieves high efficiency without compromising accuracy. I shall present the novel computational mathematics behind the efficiency gain1, and apply it for property discovery of materials. |
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