Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic...

Area of Science:

• Computational Physics and Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Traditional Kohn-Sham density functional theory (KS-DFT) calculations require computationally expensive explicit diagonalization of the Hamiltonian.
• Scaling KS-DFT to large systems (thousands of electrons) is a major challenge in computational materials science.
• Existing methods struggle with efficiency for both metallic and insulating large-scale systems.

Purpose of the Study:

• To introduce a novel iterative strategy for KS-DFT calculations applicable to large metallic and insulating systems.
• To significantly reduce the computational cost of large-scale electronic structure calculations.
• To enable efficient ab initio molecular dynamics simulations of complex materials.

Main Methods:

• Employs a two-level Chebyshev polynomial filter based complementary subspace strategy.
• Avoids explicit Hamiltonian diagonalization on every self-consistent field (SCF) iteration.
• Reduces subspace diagonalization to partially occupied states and uses an inner Chebyshev filter iteration for efficiency.

Main Results:

• The novel strategy significantly reduces computational cost for large metallic systems.
• Subspace diagonalization is eliminated entirely for insulating systems.
• The method, implemented within the discontinuous Galerkin (DG) framework, achieves chemical accuracy for systems with tens of thousands of electrons.
• Demonstrated feasibility by simulating 8,000-atom bulk silicon, achieving an average SCF step time of 51s on 34,560 processors.

Conclusions:

• The developed iterative strategy offers a computationally efficient and scalable approach for large-scale KS-DFT.
• This method is poised to advance large-scale ab initio molecular dynamics simulations.
• The approach enables rapid, accurate simulations of complex bulk and nano systems.