arXiv subjects

Lin Lin

Publications and source records attributed to Lin Lin.

At least 307 records · Page 17Linked to original sources

arXiv2016

Adaptively Compressed Exchange Operator

The Fock exchange operator plays a central role in modern quantum chemistry. The large computational cost associated with the Fock exchange operator hinders Hartree-Fock calculations and Kohn-Sham density functional theory calculations with hybrid exchange-correlation functionals, even for systems consisting of hundreds of atoms. We develop the adaptively compressed exchange operator (ACE) formulation, which greatly reduces the computational cost associated with the Fock exchange operator without loss of accuracy. The ACE formulation does not depend on the size of the band gap, and thus can be applied to insulating, semiconducting as well as metallic systems. In an iterative framework for solving Hartree-Fock-like systems, the ACE formulation only requires moderate modification of the code, and can be potentially beneficial for all electronic structure software packages involving exchange calculations. Numerical results indicate that the ACE formulation can become advantageous even for small systems with tens of atoms. In particular, the cost of each self-consistent field iteration for the electron density in the ACE formulation is only marginally larger than that of the generalized gradient approximation (GGA) calculation, and thus offers orders of magnitude speedup for Hartree-Fock-like calculations.

physics.comp-ph↗

arXiv2015

Localized spectrum slicing

Given a sparse Hermitian matrix $A$ and a real number $μ$, we construct a set of sparse vectors, each approximately spanned only by eigenvectors of $A$ corresponding to eigenvalues near $μ$. This set of vectors spans the column space of a localized spectrum slicing (LSS) operator, and is called an LSS basis set. The sparsity of the LSS basis set is related to the decay properties of matrix Gaussian functions. We present a divide-and-conquer strategy with controllable error to construct the LSS basis set. This is a purely algebraic process using only submatrices of $A$, and can therefore be applied to general sparse Hermitian matrices. The LSS basis set leads to sparse projected matrices with reduced sizes, which allows the projected problems to be solved efficiently with techniques using sparse linear algebra. As an example, we demonstrate that the LSS basis set can be used to solve interior eigenvalue problems for a discretized second order partial differential operator in one-dimensional and two-dimensional domains, as well as for a matrix of general sparsity pattern.

math.NA↗

arXiv2015

Randomized estimation of spectral densities of large matrices made accurate

For a large Hermitian matrix $A\in \mathbb{C}^{N\times N}$, it is often the case that the only affordable operation is matrix-vector multiplication. In such case, randomized method is a powerful way to estimate the spectral density (or density of states) of $A$. However, randomized methods developed so far for estimating spectral densities only extract information from different random vectors independently, and the accuracy is therefore inherently limited to $\mathcal{O}(1/\sqrt{N_{v}})$ where $N_{v}$ is the number of random vectors. In this paper we demonstrate that the "$\mathcal{O}(1/\sqrt{N_{v}})$ barrier" can be overcome by taking advantage of the correlated information of random vectors when properly filtered by polynomials of $A$. Our method uses the fact that the estimation of the spectral density essentially requires the computation of the trace of a series of matrix functions that are numerically low rank. By repeatedly applying $A$ to the same set of random vectors and taking different linear combination of the results, we can sweep through the entire spectrum of $A$ by building such low rank decomposition at different parts of the spectrum. Under some assumptions, we demonstrate that a robust and efficient implementation of such spectrum sweeping method can compute the spectral density accurately with $\mathcal{O}(N^2)$ computational cost and $\mathcal{O}(N)$ memory cost. Numerical results indicate that the new method can significantly outperform existing randomized methods in terms of accuracy. As an application, we demonstrate a way to accurately compute a trace of a smooth matrix function, by carefully balancing the smoothness of the integrand and the regularized density of states using a deconvolution procedure.

math.NA↗

arXiv2015

Experimental observation of magnetoelectricity in spin ice Dy$_2$Ti$_2$O$_7$

The intrinsic noncollinear spin patterns in rare-earth pyrochlore are physically interesting, hosting many emergent properties, e.g. spin ice and monopole-type excitation. Recently, the magnetic monopole excitation of spin ice systems was predicted to be magnetoelectric active, while rare experimental works have directly confirmed this scenario. In this work, we performed systematic experimental investigation on the magnetoelectricity of Dy$_2$Ti$_2$O$_7$ by probing the ferroelectricity, spin dynamics, and dielectric behaviors. Two ferroelectric transitions at $T_{c1}$=25 K and $T_{c2}$=13 K have been observed. Remarkable magnetoelectric coupling is identified below the lower transition temperature, with a significant suppression of the electric polarization upon applied magnetic field. It is surprised that the lower ferroelectric transition temperature just coincides with the Ising-spin paramagnetic transition point, below which the quasi-particle-like monopoles are populated, indicating implicit correlation between electric dipoles and spin moments. The possible magnetoelectric mechanisms have also been discussed although a decent theory remains unavailable up to date. Our results will stimulate more investigations to explore multiferroicity in these spin ice systems and other frustrated magnets.

cond-mat.mtrl-sci↗

arXiv2015

Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations

Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn-Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann-Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracy required in practice. Since the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann-Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi-1D and 3D disordered Si systems, vibration calculation of a quasi-1D Si system, and molecular dynamics calculations of H$_2$ and liquid Al-Si alloy systems, where we find excellent agreement with independent benchmark results in literature.

physics.comp-ph↗

arXiv2015

Plasma cleaning: A new possible treatment for niobium superconducting cavity after nitrogen doping

Nitrogen doping treatment with the subsequent electropolishing (EP) of the niobium superconducting cavity can significantly increase the cavity's quality factor up to a factor of 3. But the process of the EP removal may reintroduce hydrogen in the cavity surface, which may influence the cavity's radio frequency performance. Plasma cleaning study on niobium samples with gas mixtures of argon and oxgen intended to remove contaminations (hydrocarbons and micronicdust particles) from cavity surface to avoid field emission, was performed in Peking University. The niobium samples have been analyzed using the time of flight secondary ion mass spectrometry (TOF-SIMS) to measure the depth profiles of H, C, O, F, P and Nb. The measuring results show that the plasma cleaning with gas mixtures of argon and oxgen and conditions of about 20Pa and 100W can remarkably reduce the contents of impurity elements in the depth of about 30 nm without introducing hydrogen in the cavity surface. So plasma cleaning has been proposed to be a new possible treatment for niobium superconducting cavity after nitrogen doping.

physics.acc-ph↗

arXiv2015

DGDFT: A Massively Parallel Method for Large Scale Density Functional Theory Calculations

We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys. 2012, 231, 2140] method, for efficient large-scale Kohn-Sham DFT based electronic structure calculations. The DGDFT method uses adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field (SCF) iteration to represent the solution to the Kohn-Sham equations. The use of the ALB set provides a systematic way to improve the accuracy of the approximation. It minimizes the number of degrees of freedom required to represent the solution to the Kohn-Sham problem for a desired level of accuracy. In particular, DGDFT can reach the planewave accuracy with far fewer numbers of degrees of freedom. By using the pole expansion and selected inversion (PEXSI) technique to compute electron density, energy and atomic forces, we can make the computational complexity of DGDFT scale at most quadratically with respect to the number of electrons for both insulating and metallic systems. We show that DGDFT can achieve 80% parallel efficiency on 128,000 high performance computing cores when it is used to study the electronic structure of two-dimensional (2D) phosphorene systems with 3,500-14,000 atoms. This high parallel efficiency results from a two-level parallelization scheme that we will describe in detail.

physics.comp-ph↗

arXiv2015

A posteriori error estimates for discontinuous Galerkin methods using non-polynomial basis functions. Part I: Second order linear PDE

We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving second order linear PDEs. Our residual type upper and lower bound error estimates measure the error in the energy norm. The main merit of our method is that the method is parameter-free, in the sense that all but one solution-dependent constants appearing in the upper and lower bound estimates are explicitly computable by solving local eigenvalue problems, and the only non-computable constant can be reasonably approximated by a computable one without affecting the overall effectiveness of the estimates in practice. As a side product of our formulation, the penalty parameter in the interior penalty formulation can be automatically determined as well. We develop an efficient numerical procedure to compute the error estimators. Numerical results for a variety of problems in 1D and 2D demonstrate that both the upper bound and lower bound are effective.

math.NA↗

arXiv2015

PSelInv -- A Distributed Memory Parallel Algorithm for Selected Inversion : the Symmetric Case

We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call \texttt{PSelInv}. The \texttt{PSelInv} method computes selected elements of a general sparse matrix $A$ that can be decomposed as $A = LU$, where $L$ is lower triangular and $U$ is upper triangular. The implementation described in this paper focuses on the case of sparse symmetric matrices. It contains an interface that is compatible with the distributed memory parallel sparse direct factorization \texttt{SuperLU\_DIST}. However, the underlying data structure and design of \texttt{PSelInv} allows it to be easily combined with other factorization routines such as \texttt{PARDISO}. We discuss general parallelization strategies such as data and task distribution schemes. In particular, we describe how to exploit the concurrency exposed by the elimination tree associated with the $LU$ factorization of $A$. We demonstrate the efficiency and accuracy of \texttt{PSelInv} by presenting a number of numerical experiments. In particular, we show that \texttt{PSelInv} can run efficiently on more than $4,000$ cores for a modestly sized matrix. We also demonstrate how \texttt{PSelInv} can be used to accelerate large-scale electronic structure calculations.

math.NA↗

arXiv2015

X-ray Perspective of the Twisted Magnetospheres of Magnetars

Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are recognized as the most promising magnetar candidates, as indicated by their energetic bursts and rapid spin-downs. It is expected that the strong magnetic field leaves distinctive imprints on the emergent radiation both by affecting the radiative processes in atmospheres of magnetars and by scattering in the upper magnetospheres. We construct a self-consistent physical model that incorporates emission from the magnetar surface and its reprocessing in the three-dimensional (3D) twisted magnetosphere using a Monte Carlo technique. The synthetic spectra are characterized by four parameters: surface temperature kT, surface magnetic field strength $B$, magnetospheric twist angle $Δϕ$, and the normalized electron velocity $β$. We also create a tabular model (STEMS3D) and apply it to a large sample of XMM-Newton spectra of magnetars. The model successfully fits nearly all spectra, and the obtained magnetic field for 7 out of the 11 sources are consistent with the values inferred from the spin-down rates. We conclude that the continuum-fitting by our model is a robust method to measure the magnetic field strength and magnetospheric configuration of AXPs and SGRs. Investigating the multiple observations of variable sources, we also study the mechanism of their spectral evolution. Our results suggest that the magnetospheres in these sources are highly twisted ($Δϕ> 1$), and the behavior of magnetospheric twisting and untwisting is revealed in the 2002 outburst of 1E 2259+586.

astro-ph.HE↗

arXiv2015

Enhancing the scalability and load balancing of the parallel selected inversion algorithm via tree-based asynchronous communication

We develop a method for improving the parallel scalability of the recently developed parallel selected inversion algorithm [Jacquelin, Lin and Yang 2014], named PSelInv, on massively parallel distributed memory machines. In the PSelInv method, we compute selected elements of the inverse of a sparse matrix A that can be decomposed as A = LU, where L is lower triangular and U is upper triangular. Updating these selected elements of A-1 requires restricted collective communications among a subset of processors within each column or row communication group created by a block cyclic distribution of L and U. We describe how this type of restricted collective communication can be implemented by using asynchronous point-to-point MPI communication functions combined with a binary tree based data propagation scheme. Because multiple restricted collective communications may take place at the same time in the parallel selected inversion algorithm, we need to use a heuristic to prevent processors participating in multiple collective communications from receiving too many messages. This heuristic allows us to reduce communication load imbalance and improve the overall scalability of the selected inversion algorithm. For instance, when 6,400 processors are used, we observe over 5x speedup for test matrices. It also mitigates the performance variability introduced by an inhomogeneous network topology.

cs.DC↗

arXiv2015

Large-scale ab initio simulations based on systematically improvable atomic basis

We present a first-principles computer code package (ABACUS) that is based on density functional theory and numerical atomic basis sets. Theoretical foundations and numerical techniques used in the code are described, with focus on the accuracy and transferability of the hierarchical atomic basis sets as generated using a scheme proposed by Chen, Guo and He [J. Phys.:Condens. Matter \textbf{22}, 445501 (2010)]. Benchmark results are presented for a variety of systems include molecules, solids, surfaces, and defects. All results show that the ABACUS package with its associated atomic basis sets is an efficient and reliable tool for simulating both small and large-scale materials.

cond-mat.mtrl-sci↗

arXiv2015

P-MaNGA: Gradients in Recent Star Formation Histories as Diagnostics for Galaxy Growth and Death

We present an analysis of the data produced by the MaNGA prototype run (P-MaNGA), aiming to test how the radial gradients in recent star formation histories, as indicated by the 4000AA-break (D4000), Hdelta absorption (EW(Hd_A)) and Halpha emission (EW(Ha)) indices, can be useful for understanding disk growth and star formation cessation in local galaxies. We classify 12 galaxies observed on two P-MaNGA plates as either centrally quiescent (CQ) or centrally star-forming (CSF), according to whether D4000 measured in the central spaxel of each datacube exceeds 1.6. For each galaxy we generate both 2D maps and radial profiles of D4000, EW(Hd_A) and EW(Ha). We find that CSF galaxies generally show very weak or no radial variation in these diagnostics. In contrast, CQ galaxies present significant radial gradients, in the sense that D4000 decreases, while both EW(Hd_A) and EW(Ha) increase from the galactic center outward. The outer regions of the galaxies show greater scatter on diagrams relating the three parameters than their central parts. In particular, the clear separation between centrally-measured quiescent and star-forming galaxies in these diagnostic planes is largely filled in by the outer parts of galaxies whose global colors place them in the green valley, supporting the idea that the green valley represents a transition between blue-cloud and red-sequence phases, at least in our small sample. These results are consistent with a picture in which the cessation of star formation propagates from the center of a galaxy outwards as it moves to the red sequence.

astro-ph.GA↗

arXiv2015

Drive laser system for the DC-SRF photoinjector at Peking University

Photoinjectors are widely used for linear accelerators as electron sources to generate high-brightness electron beam. Drive laser, which determines the timing structure and quality of the electron beam, is a crucial device of photoinjector. A new drive laser system has been designed and constructed for the upgraded 3.5-cell DC-SRF photoinjector at Peking University. The drive laser system consists of a 1064 nm laser oscillator, a four- stage amplifier, the second and fourth harmonic generators, the optical system to transfer the UV pulses to the photocathode, and the synchronization system. The drive laser system has been successfully applied in the stable operation of DC-SRF photoinjector and its performance meets the requirements. 266 nm laser with an average power close to 1W can be delivered to illuminate the Cs2Te photocathode and the instability is less than 5% for long time operation. The design consideration for improving the UV laser quality, a detailed description of laser system, and its performance are presented in this paper.

physics.acc-ph↗

arXiv2015

Edge reconstruction in armchair phosphorene nanoribbons revealed by discontinuous Galerkin density functional theory

With the help of our recently developed massively parallel DGDFT (Discontinuous Galerkin Density Functional Theory) methodology, we perform large-scale Kohn-Sham density functional theory calculations on phosphorene nanoribbons with armchair edges (ACPNRs) containing a few thousands to ten thousand atoms. The use of DGDFT allows us to systematically achieve conventional plane wave basis set type of accuracy, but with a much smaller number (about 15) of adaptive local basis (ALB) functions per atom for this system. The relatively small number degrees of freedom required to represent the Kohn-Sham Hamiltonian, together with the use of the pole expansion the selected inversion (PEXSI) technique that circumvents the need to diagonalize the Hamiltonian, result in a highly efficient and scalable computational scheme for analyzing the electronic structures of ACPNRs as well as its dynamics. The total wall clock time for calculating the electronic structures of large-scale ACPNRs containing 1080-10800 atoms is only 10-25 s per self-consistent field (SCF) iteration, with accuracy fully comparable to that obtained from conventional planewave DFT calculations. For the ACPNR system, we observe that the DGDFT methodology can scale to 5,000-50,000 processors. We use DGDFT based ab-initio molecular dynamics (AIMD) calculations to study the thermodynamic stability of ACPNRs. Our calculations reveal that a 2 * 1 edge reconstruction appears in ACPNRs at room temperature.

cond-mat.mtrl-sci↗

arXiv2014

Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix

Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient and highly parallelizable method to construct a set of, optionally orthogonal, localized basis functions for the associated subspace. Our method explicitly uses the fact that density matrices associated with insulating systems decay exponentially along the off-diagonal direction in the real space representation. Our method avoids the usage of an optimization procedure, and the localized basis functions are constructed directly from a set of selected columns of the density matrix (SCDM). Consequently, the only adjustable parameter in our method is the truncation threshold of the localized basis functions. Our method can be used in any electronic structure software package with an arbitrary basis set. We demonstrate the numerical accuracy and parallel scalability of the SCDM procedure using orbitals generated by the Quantum ESPRESSO software package. We also demonstrate a procedure for combining SCDM with Hockney's algorithm to efficiently perform Hartree-Fock exchange energy calculations with near linear scaling.

physics.comp-ph↗

arXiv2014

Approximating spectral densities of large matrices

In physics, it is sometimes desirable to compute the so-called \emph{Density Of States} (DOS), also known as the \emph{spectral density}, of a real symmetric matrix $A$. The spectral density can be viewed as a probability density distribution that measures the likelihood of finding eigenvalues near some point on the real line. The most straightforward way to obtain this density is to compute all eigenvalues of $A$. But this approach is generally costly and wasteful, especially for matrices of large dimension. There exists alternative methods that allow us to estimate the spectral density function at much lower cost. The major computational cost of these methods is in multiplying $A$ with a number of vectors, which makes them appealing for large-scale problems where products of the matrix $A$ with arbitrary vectors are relatively inexpensive. This paper defines the problem of estimating the spectral density carefully, and discusses how to measure the accuracy of an approximate spectral density. It then surveys a few known methods for estimating the spectral density, and proposes some new variations of existing methods. All methods are discussed from a numerical linear algebra point of view.

math.NA↗

arXiv2014

Electronic Structure of Large-Scale Graphene Nanoflakes

With the help of the recently developed SIESTA-PEXSI method [J. Phys.: Condens. Matter \textbf{26}, 305503 (2014)], we perform Kohn-Sham density functional theory (DFT) calculations to study the stability and electronic structure of hexagonal graphene nanoflakes (GNFs) with up to 11,700 atoms. We find the electronic properties of GNFs, including their cohesive energy, HOMO-LUMO energy gap, edge states and aromaticity, depend sensitively on the type of edges (ACGNFs and ZZGNFs), size and the number of electrons. We observe that, due to the edge-induced strain effect in ACGNFs, large-scale ACGNFs' cohesive energy decreases as their size increases. This trend does not hold for ZZGNFs due to the presence of many edge states in ZZGNFs. We find that the energy gaps $E_g$ of GNFs all decay with respect to $1/L$, where $L$ is the size of the GNF, in a linear fashion. But as their size increases, ZZGNFs exhibit more localized edge states. We believe the presence of these states makes their gap decrease more rapidly. In particular, when $L$ is larger than 6.40 $nm$, we find that ZZGNFs exhibit metallic characteristics. Furthermore, we find that the aromatic structures of GNFs appear to depend only on whether the system has $4N$ or $4N+2$ electrons, where $N$ is an integer.

cond-mat.mtrl-sci↗