Sparse matrix multiplication: The distributed block-compressed sparse row library

Borštnik, Urban; VandeVondele, Joost; Weber, Valéry; Hutter, Jürg

doi:10.1016/j.parco.2014.03.012

Cited by 184 publications

(180 citation statements)

References 20 publications

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“…The matrix blocks correspond to atoms and are filtered with a threshold of 10 -6 for the Frobenius norm of the block. 57 A similar occupation of scaled density matrices has been reported in Ref. 67.…”

Section: Effect Of Sparsitysupporting

confidence: 82%

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis

Wilhelm

Seewald

Ben

et al. 2016

J. Chem. Theory Comput.

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We present an algorithm for computing the correlation energy in the random phase approximation (RPA) in a Gaussian basis requiring O(N 3 ) operations and O(N 2 ) memory. The method is based on the resolution of the identity (RI) with the overlap metric, a reformulation of RI-RPA in the Gaussian basis, imaginary time and imaginary frequency integration techniques and the use of sparse linear algebra. Additional memory reduction without extra computations can be achieved by an iterative scheme which overcomes the memory bottleneck of canonical RPA implementations. We report a massively parallel implementation which is the key for the application to large systems. Finally, cubic-scaling RPA is applied to a thousand water molecules using a correlation-consistent triple-zeta quality basis.

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Section: Effect Of Sparsitysupporting

confidence: 82%

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis

Wilhelm

Seewald

Ben

et al. 2016

J. Chem. Theory Comput.

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“…The same holds for the S and H matrices. If all multiplications are implemented using sparse matrix matrix multiplication, for example using the DBCSR library, 28 the computation of the density matrix, starting from the H and S matrix can be performed in O(N)…”

Section: Combining Linear-scaling Dft With Subsystem Dftmentioning

confidence: 99%

Combining Linear-Scaling DFT with Subsystem DFT in Born–Oppenheimer and Ehrenfest Molecular Dynamics Simulations: From Molecules to a Virus in Solution

Andermatt

Cha

Schiffmann

et al. 2016

J. Chem. Theory Comput.

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In this work, methods for the efficient simulation of large systems embedded in a molecular environment are presented. These methods combine linear-scaling (LS) Kohn-Sham (KS) density functional theory (DFT) with subsystem (SS) DFT. LS DFT is efficient for large subsystems, while SS DFT is linear scaling with a smaller prefactor for large sets of small molecules. The combination of SS and LS, which is an embedding approach, can result in a 10-fold speedup over a pure LS simulation for large systems in aqueous solution. In addition to a ground-state Born-Oppenheimer SS+LS implementation, a time-dependent density functional theory-based Ehrenfest molecular dynamics (EMD) using density matrix propagation is presented that allows for performing nonadiabatic dynamics. Density matrix-based EMD in the SS framework is naturally linear scaling and appears suitable to study the electronic dynamics of molecules in solution. In the LS framework, linear scaling results as long as the density matrix remains sparse during time propagation. However, we generally find a less than exponential decay of the density matrix after a sufficiently long EMD run, preventing LS EMD simulations with arbitrary accuracy. The methods are tested on various systems, including spectroscopy on dyes, the electronic structure of TiO2 nanoparticles, electronic transport in carbon nanotubes, and the satellite tobacco mosaic virus in explicit solution.

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“…The graph-based electronic structure theory combines the natural parallelism of a divide and conquer approach [12][13][14][15][16][17] with the automatically adaptive and tunable accuracy of a thresholded sparse matrix algebra, [18][19][20][21][22][23][24][25][26][27][28][29][30][31] which can be combined with fast, low pre-factor, recursive Fermi operator expansion methods [32][33][34][35][36][37][38][39][40][41] and can be applied to modern formulations of Born-Oppenheimer molecular dynamics. [42][43][44][45][46][47][48][49][50] The article is outlined as follows: first we introduce the graph-based formalism for general sparse matrix polynomials expanded over separate subgraphs, thereafter we apply the methodology to the Fermi-operator expansion in electronic structure theory with demonstrations for a protein-like structure of polyalanine solvated in water, before analyzing applications in molecular dynamics simulations.…”

Section: Introductionmentioning

confidence: 99%

Graph-based linear scaling electronic structure theory

Niklasson

Mniszewski

Negre

et al. 2016

The Journal of Chemical Physics

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We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license

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Sparse matrix multiplication: The distributed block-compressed sparse row library

Cited by 184 publications

References 20 publications

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis

Large-Scale Cubic-Scaling Random Phase Approximation Correlation Energy Calculations Using a Gaussian Basis

Combining Linear-Scaling DFT with Subsystem DFT in Born–Oppenheimer and Ehrenfest Molecular Dynamics Simulations: From Molecules to a Virus in Solution

Graph-based linear scaling electronic structure theory

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