Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session G27: Focus Session: Novel Computational Algorithms II |
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Sponsoring Units: DCOMP Chair: Barry Schneider, National Science Foundation Room: Baltimore Convention Center 324 |
Tuesday, March 14, 2006 8:00AM - 8:36AM |
G27.00001: Optimization of Large Scale Matrix Computations for Multi-length Scale Structured Matrices Invited Speaker: Quantum monte carlo simulation of interacting electron systems is an increasingly powerful tool in investigating many of the most fundamental properties of materials, such as their magnetic and optical response, and conductivity. However, the simulations are currently limited to a few hundred particles. The primary bottleneck is the calculation of the inverse of a multi-length and highly structured matrix. In this talk, we will report our recent progress on this problem. We first present a semi-direct solver which is numerically stable and robust by a novel self-adapting block cyclic reduction technique depending on the parameters of the problem. The new solver is more than an order of magnitude faster than existing techniques. Then we will present robust preconditioning techniques in iterative solvers which can effectively precondition the matrices at much stronger coupling and lower temperatures than had hitherto been possible. [Preview Abstract] |
Tuesday, March 14, 2006 8:36AM - 8:48AM |
G27.00002: Equilibration of walkers and correlation of samples in QMC simulations D. Nissenbaum, B. Barbiellini, A. Bansil When using the Metropolis algorithm from an unequilibrated starting point to obtain properly distributed samples for a Quantum Monte Carlo (QMC) calculation, and when analyzing the accuracy of the results after equilibration, one needs to properly handle two factors: the time taken for the walkers to equilibrate, and the presence of correlations in the sample points after the walkers have equilibrated. Inclusion of unequilibrated data gives a bias to the computed averages, while dealing appropriately with correlated data is essential in order to obtain accurate error bars. In this connection, we are developing reliable techniques to determine equilibration time and compute observable error bars. We present a careful study of several Li clusters, ranging from the Li dimer to a cluster containing 64 Li atoms, and focus particularly on scaling properties of the equilibration time with the size of the system. Work supported in part by the USDOE. [Preview Abstract] |
Tuesday, March 14, 2006 8:48AM - 9:00AM |
G27.00003: Configuration Space Renormalization (CSR): a study of fractional quantization of charge in a dual-edge fractional quantum Hall system. Eugene Tsiper A renormalization procedure is designed to find a subspace of high
relevance in a many-body Hilbert space. Substantial reduction in the
basis size can be achieved while approaching the exact
diagonalization
results. The idea is to search for a set of many-particle
configurations that contribute the largest weight to the exact
solution of the many-body Schr\"odinger equation, without actually
computing the exact solution.
We start with some suitable set of $K$ configurations and find the
ground state of the Hamiltonian in the many-body subspace that they
span. We then retain $K' |
Tuesday, March 14, 2006 9:00AM - 9:12AM |
G27.00004: New eigensolvers and preconditioners for large scale nanoscience simulations Andrew Canning, Osni Marques , Lin-Wang Wang , Christof Voemel, Stanimire Tomov, Julien Langou First-principles materials science calculations typically involve a self-consistent solution of the Kohn-Sham equations. These types of methods typically scale with the cube of the system size and can only be used to study systems of up to a thousand atoms. To study larger systems we use semi-empirical potentials or approximated ab initio potentials such as those constructed using the charge patching method. Using these types of potentials does not require a selfconsistent solution of our effective single particle equations and we can solve directly for the few states of interest around the gap. This leads to a method that is effectively O(N) if we consider the number of states we require to be fixed as the system size increases. The solution of our single particle equations now becomes an interior eigenvalue problem for a few states around a given energy rather than the self-consistent solution for the lowest n states where n is the number of bands. I will compare different methods (conjugate gradient, Jacobi-Davidson, Lanczos) for this problem with particular emphasis on solving large nanosystems on parallel computers. Work supported by the DOE under the Modeling and Simulation in Nanoscience Initiative. [Preview Abstract] |
Tuesday, March 14, 2006 9:12AM - 9:48AM |
G27.00005: Turbocharging time-dependent density-functional theory with Lanczos chains Invited Speaker: Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is represented by a matrix continued- fraction whose coefficients can be obtained from the non-symmetric block- Lanczos method. The resulting algorithm, which is particularly convenient when large basis sets are used, allows for the calculation of the full spectrum of a system with a computational workload only a few times larger than needed for static polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with calculation of the spectrum of benzene and of fullerene, and prospects for its application to the large-scale calculation of optical spectra are discussed. [Preview Abstract] |
Tuesday, March 14, 2006 9:48AM - 10:00AM |
G27.00006: Large-Scale First-Principles Molecular Dynamics Simulations on the BlueGene/L Computer Francois Gygi, Erik W. Draeger We present the results of large-scale First-Principles Molecular Dynamics (FPMD) simulations performed on the BlueGene/L computer, using up to 65,536 processors. Simulations involving 1000 molybdenum atoms were carried out using the Qbox code with non-local, norm-conserving pseudopotentials. A parallel efficiency of 85{\%} can be attained when solving the same problem on partitions ranging from 512 nodes to 32,768 nodes. When using 65,536 processors, a floating point performance of 64 Tflops is reached. Optimization of the logical-to-physical mapping of tasks is essential in order to achieve this performance on the BlueGene/L torus architecture. We discuss the challenges encountered when implementing FPMD in the plane-wave, pseudopotential formalism on 10,000 processors and beyond. Part of this work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48. [Preview Abstract] |
Tuesday, March 14, 2006 10:00AM - 10:12AM |
G27.00007: Linear Scaling First-Principles Molecular Dynamics with Plane Waves accuracy Jean-Luc Fattebert, Francois Gygi As an alternative to the Plane Waves (PW) approach for highly accurate and unbiased Density Functional Theory molecular dynamics simulations with pseudopotentials, we propose to use a real-space finite differences discretization and a localized orbitals representation of the electronic structure. As in the PW approach, the discretization error can be reduced systematically by decreasing the mesh spacing, while the truncation error due to orbitals localization constraints decreases exponentially with the size of the localization regions. Accurate atomic forces can be computed and allow microcanonical molecular dynamics simulations. Using a supercell of 512 water molecules, we demonstrate an excellent energy conservation for localization regions large enough. We propose an explanation for the negative energy drift observed for smaller radii based on the presence of local minimas. Our implementation demonstrates an effective scaling complexity close to linear with the system size and a good parallel scaling with the number of processor [Preview Abstract] |
Tuesday, March 14, 2006 10:12AM - 10:24AM |
G27.00008: Basis set limit and systematic errors in local-orbital based all-electron DFT Volker Blum, J\"org Behler, Ralf Gehrke, Karsten Reuter, Matthias Scheffler With the advent of efficient integration schemes,$^{1,2}$ numeric atom-centered orbitals (NAO's) are an attractive basis choice in practical density functional theory (DFT) calculations of nanostructured systems (surfaces, clusters, molecules). Though all-electron, the efficiency of practical implementations promises to be on par with the best plane-wave pseudopotential codes, while having a noticeably higher accuracy if required: Minimal-sized effective tight-binding like calculations and chemically accurate all-electron calculations are both possible within the same framework; non-periodic and periodic systems can be treated on equal footing; and the localized nature of the basis allows in principle for $O(N)$-like scaling. However, converging an observable with respect to the basis set is less straightforward than with competing systematic basis choices (e.g., plane waves). We here investigate the basis set limit of optimized NAO basis sets in all-electron calculations, using as examples small molecules and clusters (N$_{2}$, Cu$_{2}$, Cu$_{4}$, Cu$_{10}$). meV-level total energy convergence is possible using $\le$50~basis functions per atom in all cases. We also find a clear correlation between the errors which arise from underconverged basis sets, and the system geometry (interatomic distance). \\ $^1$ B. Delley, J. Chem. Phys. \textbf{92}, 508 (1990), $^2$ J.M. Soler \emph{et al.}, J. Phys.: Condens. Matter \textbf{14}, 2745 (2002). [Preview Abstract] |
Tuesday, March 14, 2006 10:24AM - 10:36AM |
G27.00009: Iterative Optimized Effective Potential and Exact Exchange Calculations at Finite Temperature N.A. Modine, R.A. Lippert, A.F. Wright, R.P. Muller, M.P. Sears, A.E. Mattsson, M.P. Desjarlais We report the implementation of an iterative scheme for calculating the Optimized Effective Potential (OEP). Given an energy functional that depends explicitly on the Kohn-Sham wave functions, and therefore, implicitly on the local effective potential appearing in the Kohn-Sham equations, a gradient-based minimization is used to find the potential that minimizes the energy. Previous work has shown how to find the gradient of such an energy with respect to the effective potential in the zero-temperature limit. We discuss a density-matrix-based derivation of the gradient that generalizes the previous results to the finite temperature regime, and we describe important optimizations used in our implementation. We have applied our OEP approach to the Hartree-Fock energy expression to perform Exact Exchange (EXX) calculations. We report our EXX results for common semiconductors and ordered phases of hydrogen at zero and finite electronic temperatures. We also discuss issues involved in the implementation of forces within the OEP/EXX approach. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE- AC04-94AL85000. [Preview Abstract] |
Tuesday, March 14, 2006 10:36AM - 10:48AM |
G27.00010: Towards an exact treatment of exchange and correlation in materials: Application to CO adsorption at tran\-sition-metal surfaces Matthias Scheffler, Qing Miao Hu, Karsten Reuter We present an efficient scheme to correct the errors of density-functional theory (DFT) exchange-correlation (xc) functionals. The method locally corrects the xc interaction by analyzing clusters of the same local geometry as that of the calculations for the extended system. {\bf The correction} is found to rapidly approach a universal dependence with cluster size, exhibiting a simple analytical behavior. As a consequence it is shown how high-quality cluster studies (e.g. using B3LYP, HF+MP2, or QMC) can be used to determine the DFT-LDA/GGA error for extended systems. The method is particularly efficient for defects in the bulk and at surfaces. --- The approach is applied to CO adsorption at transition metals, where present xc functionals dramatically fail to predict the correct adsorption site.[1] The correct (experimentally confirmed) geometry is obtained by the correction scheme, and the origin of the LDA/GGA failure is discussed.\newline \newline [1] P.J. Feibelman, B. Hammer, J.K. Norskov, F. Wagner, M. Scheffler, R. Stumpf, R. Watwe, and J. Dumesic, The CO/Pt(111) puzzle. J. Phys. Chem. B {\textbf 105}, 4018 (2001). [Preview Abstract] |
Tuesday, March 14, 2006 10:48AM - 11:00AM |
G27.00011: Efficient Method for Electron-Phonon Coupling in Molecules and Nanoscale Systems Ben Powell, Mark Pederson, Tunna Baruah The coupling between electrons and phonons plays important roles in physics, chemistry and biology. However, the accurate calculation of the electron-phonon coupling constants is computationally expensive as it can involve solving the Schr\"odinger equation for ${\cal O}(3N)$ nuclear configurations, where $N$ is the number of nuclei. In analogy to the efficient field-induced extraction of IR and Raman spectra in molecules,[1] consideration of charge-induced changes in Hellman-Feynman forces as a function of electronic charge allows determination of all HOMO and LUMO electron-phonon coupling constants, including isotope dependencies, with only two SCF calculations {\it regardless of system size}.[2] The approach can also be used for electron-phonon interactions associated with other electronic states. The relation of this method to Janak's theorem[3] is discussed. This ${\cal O}(1)$ approach is numerically very stable and produces accurate results for electron-phonon coupling constants in tests on approximately 15-20 molecules ranging in size from H$_2$ to C$_{60}$. Adiabatic ionization potentials and relaxed Hubbard U parameters are presented as an example of the method. \newline [1]D.V. Porezag and M.R. Pederson, Phys. Rev. B {\bf 54}, 7830 (1996). \newline [2]B.J. Powell, M.R. Pederson and T. Baruah (submitted). \newline [3] J.F. Janak, Phys. Rev. B {\bf 18}, 7165 (1978). [Preview Abstract] |
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