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

Stephan Mohr1, William Dawson2, Michael Wagner1

  • 1Barcelona Supercomputing Center (BSC) , 08034 Barcelona, Spain.

Journal of Chemical Theory and Computation
|September 6, 2017
PubMed
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We introduce CheSS, a Chebyshev Sparse Solvers library for large-scale electronic structure calculations. This efficient solver exploits matrix sparsity for linear scaling, outperforming other methods for specific matrix properties.

Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Materials Science

Background:

  • Large-scale electronic structure calculations are computationally intensive.
  • Localized basis sets are often used to manage complexity.
  • Efficient solvers are crucial for advancing computational capabilities.

Purpose of the Study:

  • To present CheSS, a novel Chebyshev Sparse Solvers library.
  • To enable efficient solutions for large-scale electronic structure problems.
  • To leverage Chebyshev polynomial expansions for computational advantage.

Main Methods:

  • Development of the Chebyshev Sparse Solvers (CheSS) library.
  • Implementation of Chebyshev polynomial expansions for matrix operations.
  • Exploitation of matrix sparsity and linear scaling properties.

Related Experiment Videos

  • Coupling CheSS with the Density Functional Theory (DFT) code BigDFT.

    • Main Results:

    • CheSS efficiently calculates density matrices and matrix powers.
    • Eigenvalue extraction within selected intervals is supported.
    • Linear scaling with the number of non-zero entries achieved.
    • Demonstrated superior performance for matrices with small spectral widths.
    • Massively parallelizable with excellent scaling up to thousands of cores.

    Conclusions:

    • CheSS provides an efficient and scalable solution for electronic structure calculations.
    • The Chebyshev polynomial approach is effective for sparse matrices with small spectral widths.
    • Integration with DFT codes like BigDFT is feasible and beneficial.
    • The library shows significant potential for advancing large-scale computational science.