Parallel pseudospectral electronic structure: I. Hartree-Fock calculations

Chasman, David; Beachy, Michael D.; Wang, Limin; Friesner, Richard A.

doi:10.1002/(sici)1096-987x(19980715)19:9<1017::aid-jcc3>3.0.co;2-t

Cited by 19 publications

(25 citation statements)

References 23 publications

(14 reference statements)

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“…The parallel pseudo spectral algorithm has been described in our previous study, and we shall only present the basic idea without detailed elaboration. In PS algorithm, the Coulomb matrix ( J ) elements and the exchange matrix ( K ) elements are calculated via,

J_{i j} = \underset{g}{false\sum} Q_{i} false(r_{g} false) \underset{μ ν}{false\sum} ρ_{ν μ} A_{μ ν} (|, r_{g}) R_{j} false(r_{g} false)

K_{i j} = \underset{g}{false\sum} Q_{i} false(r_{g} false) \underset{μ ν}{false\sum} ρ_{ν μ} A_{μ j} (|, r_{g}) R_{ν} false(r_{g} false)

where

ρ_{ν μ}

is an element of the density matrix,

R_{j} true(r_{g} true)

is the atomic basis function j evaluated at a grid point

r_{g}

A_{μ ν} (|, r_{g})

is a three‐center, one‐electron integral representing the field at

r_{g}

due to the product of two atomic basis functions indexed by

μ

and

ν

, and

Q_{i} true(r_{g} true)

is the least squares fitting operator given by,

…”

Section: Parallel Implementationmentioning

confidence: 99%

Efficient simulation of large materials clusters using the jaguar quantum chemistry program: Parallelization and wavefunction initialization

Zhang

Weisman

Saitta

et al. 2015

Int J of Quantum Chemistry

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An outline of the improvements to the pseudospectral electronic structure program Jaguar is presented, showing efficient and robust performance of hybrid‐DFT calculations for large systems with thousands of basis functions, focusing on materials applications. The improvements include re‐engineered parallelization, the design of a fragment‐based initial guess generation method, and the validation of small eigenvalue cutoff values. An OpenMP/MPI hybrid parallelization has been implemented for the pseudospectral algorithm, which extends Jaguar's scalability to up to 256 cores in tests of TiO2 clusters with 1295‐4961 basis functions. In the largest test case, the code delivers 84.4× speedup for 128 cores in total calculation time. In addition, a fragment‐based initial guess method has been constructed for large systems containing many transition metals, where the conventional (atomic) approach often fails. Overall, Jaguar is now capable of efficiently and robustly performing hybrid‐DFT geometrical optimizations for large systems with more than 600 atoms in reasonable runtimes. © 2015 Wiley Periodicals, Inc.

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J_{i j} = \underset{g}{false\sum} Q_{i} false(r_{g} false) \underset{μ ν}{false\sum} ρ_{ν μ} A_{μ ν} (|, r_{g}) R_{j} false(r_{g} false)

K_{i j} = \underset{g}{false\sum} Q_{i} false(r_{g} false) \underset{μ ν}{false\sum} ρ_{ν μ} A_{μ j} (|, r_{g}) R_{ν} false(r_{g} false)

where

ρ_{ν μ}

is an element of the density matrix,

R_{j} true(r_{g} true)

is the atomic basis function j evaluated at a grid point

r_{g}

A_{μ ν} (|, r_{g})

is a three‐center, one‐electron integral representing the field at

r_{g}

due to the product of two atomic basis functions indexed by

μ

and

ν

, and

Q_{i} true(r_{g} true)

is the least squares fitting operator given by,

…”

Section: Parallel Implementationmentioning

confidence: 99%

Efficient simulation of large materials clusters using the jaguar quantum chemistry program: Parallelization and wavefunction initialization

Zhang

Weisman

Saitta

et al. 2015

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

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“…However, the cost of task sorting is not to be neglected, see Figure 3b. With the plain WS approach in the range from 128 to 2048 cores the scheduling overhead does not contribute much to the overall effort, slowly increasing from 0.1 to 1.2 s in calculations on Cu 10 . Yet, for the methods with CS, it is notably higher, rising from 10 to 141 s for CS1ST and from 42 to 352 s for CS1WS.…”

Section: Small Copper Clustersmentioning

confidence: 99%

“…In quantum chemistry calculations, many algorithms involve independent subtasks that in principle are easy to parallelize, but often are not equally compute‐intensive. To tackle these tasks, various parallelization strategies have been invoked …”

Section: Introductionmentioning

confidence: 99%

“…The simplest method for distributing tasks over several processors is to assign the tasks statically, static task distribution (ST), to the various processes . This strategy can be quite efficient, for example, for fine‐grained tasks with very similar or even identical time requirements.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8][9][10] The simplest method for distributing tasks over several processors is to assign the tasks statically, static task distribution (ST), to the various processes. [8,[10][11][12][13] This strategy can be quite efficient, for example, for fine-grained tasks with very similar or even identical time requirements. If tasks demand (widely) varying amounts of work, such a static strategy can also be efficiently used if the time of each task can be accurately estimated or the number of tasks is sufficiently large to admit an essentially even load distribution for statistical reasons.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Load balancing by work–stealing in quantum chemistry calculations: Application to hybrid density functional methods

Nikodem

Matveev

Soini

et al. 2014

Int J of Quantum Chemistry

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Parallel implementations of quantum chemistry programs targeting supercomputers are challenging applications of dynamic load balancing algorithms. The implementation of work stealing (WS) algorithms is discussed and their usefulness is demonstrated. Evaluation of the four‐center integrals of a Cu10 cluster requires 25 core‐hours overall, achieving 88% efficiency with simple WS for 2048 cores, and 97% with task presorting based on a cost estimate. Limitations of cost sorting become noticeable for larger systems. When spatial symmetry is exploited together with integral screening, bundling the original tasks yields an efficiency of 98% for Cu79 in Oh symmetry on 512, 1204, and 2048 cores. The advantage of WS algorithms described in this work is not limited to the evaluation of four‐center integrals. © 2014 Wiley Periodicals, Inc.

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Use of STOs in Hartree-Fock calculations: Error analysis and variance-minimized pseudospectral method

Kennedy

Zhao

1999

J. Comput. Chem.

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In this study it is demonstrated that STO (Slater‐type orbital) basis sets are particularly well suited to pseudospectral Hartree–Fock calculations. The reduction of two‐electron integrals, to ones that are (at worst) equivalent to a one‐electron integral over three centers, eliminates the need for slowly convergent one‐center expansions. This allows all integrals to be calculated quickly and accurately in either spherical or ellipsoidal coordinates. A new variance‐minimized variant of the pseudospectral method is derived and applied to a number of small closed‐shell molecules. The performance of the algorithm is assessed relative to purely spectral calculations employing STO and GTO (Gaussian‐type orbital) basis sets. The pseudospectral operator is used to assess the errors contained in solutions found by the purely spectral method. The suitability of a number of different de‐aliasing set types is also examined. Orthogonal sets of hydrogen‐like eigenfunctions were found to be optimal. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1537–1548, 1999

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Parallel pseudospectral electronic structure: I. Hartree-Fock calculations

Cited by 19 publications

References 23 publications

Efficient simulation of large materials clusters using the jaguar quantum chemistry program: Parallelization and wavefunction initialization

Efficient simulation of large materials clusters using the jaguar quantum chemistry program: Parallelization and wavefunction initialization

Load balancing by work–stealing in quantum chemistry calculations: Application to hybrid density functional methods

Use of STOs in Hartree-Fock calculations: Error analysis and variance-minimized pseudospectral method

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