arXiv subjects

Weile Jia

Publications and source records attributed to Weile Jia.

42 records · Page 3Linked to original sources

arXiv2019

Fast real-time time-dependent hybrid functional calculations with the parallel transport gauge and the adaptively compressed exchange formulation

We present a new method to accelerate real time-time dependent density functional theory (rt-TDDFT) calculations with hybrid exchange-correlation functionals. For large basis set, the computational bottleneck for large scale calculations is the application of the Fock exchange operator to the time-dependent orbitals. Our main goal is to reduce the frequency of applying the Fock exchange operator, without loss of accuracy. We achieve this by combining the recently developed parallel transport (PT) gauge formalism and the adaptively compressed exchange operator (ACE) formalism. The PT gauge yields the slowest possible dynamics among all choices of gauge. When coupled with implicit time integrators such as the Crank-Nicolson (CN) scheme, the resulting PT-CN scheme can significantly increase the time step from sub-attoseconds to 10-100 attoseconds. At each time step $t_{n}$, PT-CN requires the self-consistent solution of the orbitals at time $t_{n+1}$. We use ACE to delay the update of the Fock exchange operator in this nonlinear system, while maintaining the same self-consistent solution. We verify the performance of the resulting PT-CN-ACE method by computing the absorption spectrum of a benzene molecule and the response of bulk silicon systems to an ultrafast laser pulse, using the planewave basis set and the HSE functional. We report the strong and weak scaling of the PT-CN-ACE method for silicon systems ranging from 32 to 1024 atoms, with up to 2048 computational cores. Compared to standard explicit time integrators such as the 4th order Runge-Kutta method (RK4), the PT-CN-ACE can reduce the Fock exchange operator application by nearly 70 times, thus reduce the overall wall clock time time by 46 times for the system with 1024 atoms. Hence our work enables hybrid functional rt-TDDFT calculations to be routinely performed with a large basis set for the first time.

physics.comp-ph↗

arXiv2018

Fast real-time time-dependent density functional theory calculations with the parallel transport gauge

Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation due to the fast oscillation of electron wavefunctions, which significantly limits its range of applicability for the study of ultrafast dynamics. In this paper, we demonstrate that such oscillation can be considerably reduced by optimizing the gauge choice using the parallel transport formalism. RT-TDDFT calculations can thus be significantly accelerated using a combination of the parallel transport gauge and implicit integrators, and the resulting scheme can be used to accelerate any electronic structure software that uses a Schrödinger representation. Using absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations for example, we show that the new method can utilize a time step that is on the order of $10\sim 100$ attoseconds in a planewave basis set, and is no less than $5\sim 10$ times faster when compared to the standard explicit 4th order Runge-Kutta time integrator. Thanks to the significant increase of the size of the time step, we also demonstrate that the new method is more than 10 times faster in terms of the wall clock time when compared to the standard explicit 4th order Runge-Kutta time integrator for silicon systems ranging from 32 to 1024 atoms

physics.comp-ph↗

arXiv2017

Robust Determination of the Chemical Potential in the Pole Expansion and Selected Inversion Method for Solving Kohn-Sham density functional theory

Fermi operator expansion (FOE) methods are powerful alternatives to diagonalization type methods for solving Kohn-Sham density functional theory (KSDFT). One example is the pole expansion and selected inversion (PEXSI) method, which approximates the Fermi operator by rational matrix functions and reduces the computational complexity to at most quadratic scaling for solving KSDFT. Unlike diagonalization type methods, the chemical potential often cannot be directly read off from the result of a single step of evaluation of the Fermi operator. Hence multiple evaluations are needed to be sequentially performed to compute the chemical potential to ensure the correct number of electrons within a given tolerance. This hinders the performance of FOE methods in practice. In this paper we develop an efficient and robust strategy to determine the chemical potential in the context of the PEXSI method. The main idea of the new method is not to find the exact chemical potential at each self-consistent-field (SCF) iteration iteration, but to dynamically and rigorously update the upper and lower bounds for the true chemical potential, so that the chemical potential reaches its convergence along the SCF iteration. Instead of evaluating the Fermi operator for multiple times sequentially, our method uses a two-level strategy that evaluates the Fermi operators in parallel. In the regime of full parallelization, the wall clock time of each SCF iteration is always close to the time for one single evaluation of the Fermi operator, even when the initial guess is far away from the converged solution. We demonstrate the effectiveness of the new method using examples with metallic and insulating characters, as well as results from ab initio molecular dynamics.

physics.comp-ph↗

arXiv2017

ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.

physics.comp-ph↗

arXiv2016

SGO: An ultrafast engine for ab initio atomic structure global optimization by differential evolution

This paper presents a fast method for global search of atomic structures at ab initio level. The structures global optimization (SGO) engine consists of a high-efficiency differential evolution algorithm, accelerated local relaxation methods and an ultrafast plane-wave density functional theory code run on GPU machines. It can search the global-minimum configurations of crystals, two-dimensional materials and quantum clusters without symmetry restriction in a very short time (half or several hours). The engine is also able to search the energy landscape of a given system, which is useful for exploration of materials properties for emerging applications. The exploration of carbon monolayer and platinum atomic clusters found several new stable configurations.

cond-mat.mtrl-sci↗

arXiv2016

A Left-Looking Selected Inversion Algorithm and Task Parallelism on Shared Memory Systems

Given a sparse matrix $A$, the selected inversion algorithm is an efficient method for computing certain selected elements of $A^{-1}$. These selected elements correspond to all or some nonzero elements of the LU factors of $A$. In many ways, the type of matrix updates performed in the selected inversion algorithm is similar to that performed in the LU factorization, although the sequence of operation is different. In the context of LU factorization, it is known that the left-looking and right-looking algorithms exhibit different memory access and data communication patterns, and hence different behavior on shared memory and distributed memory parallel machines. Corresponding to right-looking and left-looking LU factorization, selected inversion algorithm can be organized as a left-looking and a right-looking algorithm. The parallel right-looking version of the algorithm has been developed in [1]. The sequence of operations performed in this version of the selected inversion algorithm is similar to those performed in a left-looking LU factorization algorithm. In this paper, we describe the left-looking variant of the selected inversion algorithm, and based on task parallel method, present an efficient implementation of the algorithm for shared memory machines. We demonstrate that with the task scheduling features provided by OpenMP 4.0, the left-looking selected inversion algorithm can scale well both on the Intel Haswell multicore architecture and on the Intel Knights Corner (KNC) manycore architecture. Compared to the right-looking selected inversion algorithm, the left-looking formulation facilitates pipelining of work along different branches of the elimination tree, and can be a promising candidate for future development of massively parallel selected inversion algorithms on heterogeneous architecture.

cs.MS↗