CheFSI

Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn-Sham equation. First-principles {it density functional theory} (DFT) calculations for the electronic structure problem require a solution of the Kohn-Sham equation, which requires one to solve a nonlinear eigenvalue problem. Solving the eigenvalue problem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshev-filtered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors and results in a significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original formulation of the CheFSI method utilizes a sparse iterative diagonalization at the first SCF step to provide initial vectors for subspace filtering at latter SCF steps. This diagonalization is expensive for large scale problems. We develop a new initial filtering step to avoid completely this diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps. Our new approach saves memory usage and can be two to three times faster than the original CheFSI method.


References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Temizer, İ.; Motamarri, P.; Gavini, V.: NURBS-based non-periodic finite element framework for Kohn-Sham density functional theory calculations (2020)
  2. Lin, Lin; Lu, Jianfeng; Ying, Lexing: Numerical methods for Kohn-Sham density functional theory (2019)
  3. Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef: The eigenvalues slicing library (EVSL): algorithms, implementation, and software (2019)
  4. Li, Yingzhou; Lin, Lin: Globally constructed adaptive local basis set for spectral projectors of second order differential operators (2019)
  5. Breuer, Alex; Wang, Xin-Cindy: More robust Chebyshev filtering for SCF iteration, with applications in real-space DFT (2018)
  6. Ghosh, Swarnava; Suryanarayana, Phanish: SPARC: accurate and efficient finite-difference formulation and parallel implementation of density functional theory: isolated clusters (2017)
  7. Ghosh, Swarnava; Suryanarayana, Phanish: SPARC: accurate and efficient finite-difference formulation and parallel implementation of density functional theory: extended systems (2017)
  8. Michaud-Rioux, Vincent; Zhang, Lei; Guo, Hong: RESCU: a real space electronic structure method (2016)
  9. Teng, Zhongming; Zhou, Yunkai; Li, Ren-Cang: A block Chebyshev-Davidson method for linear response eigenvalue problems (2016)
  10. Zhou, Yunkai; Wang, Zheng; Zhou, Aihui: Accelerating large partial EVD/SVD calculations by filtered block Davidson methods (2016)
  11. Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D.: A spectral scheme for Kohn-Sham density functional theory of clusters (2015)
  12. Zhou, Yunkai; Chelikowsky, James R.; Saad, Yousef: Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn-Sham equation (2014)