Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.

@article{Mohr2017EfficientCO,
  title={Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.},
  author={Stephan Mohr and William Dawson and Michael Wagner and Damien Caliste and Takahito Nakajima and Luigi Genovese},
  journal={Journal of chemical theory and computation},
  year={2017},
  volume={13 10},
  pages={
          4684-4698
        }
}
We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity… 

A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices

The submatrix method is presented, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications and allows imprecision in the final result in order to utilize the sparsity of the input matrix and to allow massively parallel execution.

Inverse Factorization in Electronic Structure Theory : Analysis and Parallelization

This thesis focuses on different aspects of a computational problem of inverse factorization of Hermitian positive definite matrices, and discusses a few parallel programming models with focus on task-based models, and, more specifically, the Chunks and Tasks model.

Sparse approximate matrix multiplication in a fully recursive distributed task-based parallel framework

This paper considers parallel implementations of approximate multiplication of large matrices with exponential decay of elements in computations related to electronic structure calculations and some other fields of science, and the absolute error asymptotic behavior is derived.

Flexibilities of wavelets as a computational basis set for large-scale electronic structure calculations.

It is shown how the localized description of the KS problem, emerging from the features of the basis set, is helpful in providing a simplified description of large-scale electronic structure calculations, including the SARS-CoV-2 main protease.

Complexity Reduction in Density Functional Theory Calculations of Large Systems: System Partitioning and Fragment Embedding.

A systematic complexity reduction methodology which can break down large systems into their constituent fragments, and quantify inter-fragment interactions is presented.

Roadmap on Electronic Structure Codes in the Exascale Era

This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.

Siesta: Recent developments and applications.

The more recent implementations of Siesta are described, which include full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, density functional theory (DFT)+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient van der Waals non-local density functional, and enhanced molecular-dynamics options.

A quantum advantage for Density Functional Theory ?

This work investigates the benefit of quantum computers to scale up not only manybody wavefunction methods, but also mean-field-type methods, and consequently the all range of application of quantum chemistry.

References

SHOWING 1-10 OF 70 REFERENCES

A Fast Parallel Algorithm for Selected Inversion of Structured Sparse Matrices with Application to 2D Electronic Structure Calculations

An efficient parallel algorithm and its implementation for computing the diagonal of H^-1, where H is a 2D Kohn-Sham Hamiltonian discretized on a rectangular domain using a standard second order finite difference scheme, and how elimination tree is used to organize the parallel computation.

SIESTA-PEXSI: massively parallel method for efficient and accurate ab initio materials simulation without matrix diagonalization

The performance and accuracy of the SIESTA-PEXSI method is demonstrated using several examples of large scale electronic structure calculations, including 1D, 2D and bulk problems with insulating, semi-metallic, and metallic character.

Assessment of density matrix methods for linear scaling electronic structure calculations

Purification and minimization methods for linear scaling computation of the one-particle density matrix for a fixed Hamiltonian matrix are compared and it is investigated how the convergence speed for the different methods depends on the eigenvalue distribution in theHamiltonian matrix.

Systematic sparse matrix error control for linear scaling electronic structure calculations

The effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification is studied and a way to reduce the initial exponential growth of this error is presented.

Introducing ONETEP: linear-scaling density functional simulations on parallel computers.

ONETEP is based on the reformulation of the plane wave pseudopotential method which exploits the electronic localization that is inherent in systems with a nonvanishing band gap and has the potential to provide quantitative theoretical predictions for problems involving thousands of atoms such as those often encountered in nanoscience and biophysics.

Semiempirical Molecular Dynamics (SEMD) I: Midpoint-Based Parallel Sparse Matrix-Matrix Multiplication Algorithm for Matrices with Decay.

A novel, highly efficient, and massively parallel implementation of the sparse matrix-matrix multiplication algorithm inspired by the midpoint method that is suitable for matrices with decay, and can be effectively used for the construction of the density matrix in electronic structure theory.

Accurate and efficient linear scaling DFT calculations with universal applicability.

This work uses an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis to obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large system with linear scaling walltimes requiring only a moderate demand of computing resources.

Comparison of Conjugate Gradient Density Matrix Search and Chebyshev Expansion Methods for Avoiding Diagonalization in Large-Scale Electronic Structure Calculations

A comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms and it is shown that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.

The spectral transformation Lánczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems

It is shown that for each shift several eigenvectors will converge after very few steps of the Lanczos algorithm, and the most effective combination of shifts and Lanczos runs is determined for different sizes and sparsity properties of the matrices.

Daubechies wavelets for linear scaling density functional theory.

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an
...