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Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration.

Yunkai Zhou1, Yousef Saad, Murilo L Tiago

  • 1Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA. yzhou@smu.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
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A new parallel nonlinear Chebyshev-filtered subspace iteration method significantly speeds up density functional theory (DFT) calculations. This approach accelerates solving the Kohn-Sham eigenvalue problem, enabling previously infeasible complex DFT computations.

Area of Science:

  • Computational physics
  • Quantum chemistry
  • Materials science

Background:

  • The Kohn-Sham eigenvalue problem is computationally intensive in self-consistent density functional theory (DFT).
  • Existing methods often rely on computationally expensive explicit eigenvector calculations at each self-consistent-field (SCF) iteration.

Purpose of the Study:

  • To present a parallel implementation of a nonlinear Chebyshev-filtered subspace iteration method for DFT.
  • To demonstrate the method's efficiency and scalability in a multi-processor environment.

Main Methods:

  • A nonlinear Chebyshev-filtered subspace iteration technique is employed, avoiding explicit eigenvector computation after the initial SCF iteration.
  • The method reformulates the Kohn-Sham equation solution as a nonlinear subspace iteration.

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  • Implementation in a parallel computing environment is discussed.

    • Main Results:

    • The method achieves self-consistency in a comparable number of SCF iterations to traditional eigensolver-based approaches.
    • Significant speedups are observed compared to standard diagonalization methods due to Chebyshev subspace filtering.
    • Numerical results confirm the feasibility of performing challenging DFT calculations previously considered infeasible.

    Conclusions:

    • The parallel nonlinear Chebyshev-filtered subspace iteration method offers a substantial computational advantage for DFT.
    • This approach enhances the capability to tackle complex materials science and quantum chemistry problems.
    • The implementation enables efficient large-scale DFT simulations on multi-processor systems.