Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Area of Science:

• Computational Materials Science
• Quantum Mechanics
• Density Functional Theory

Background:

• Kohn-Sham density functional theory (DFT) calculations are crucial for material modeling but are computationally intensive.
• Traditional methods involve solving nonlinear eigenvalue problems with cubic scaling complexity.
• Iterative projection methods are efficient but face bottlenecks in Rayleigh-Ritz projection and subspace diagonalization for large systems.

Purpose of the Study:

• To explore polynomial expansion approaches, specifically recursive Fermi-operator expansion, as an alternative to subspace diagonalization.
• To reduce the computational cost associated with large-scale DFT calculations.
• To compare the performance of these novel methods against traditional diagonalization techniques.

Main Methods:

• Implementation and testing of various recursive polynomial expansion algorithms.
• Detailed comparison with explicit diagonalization methods.
• Performance evaluation on both central processing unit (CPU) and graphics processing unit (GPU) architectures.
• Assessment of accuracy, computational efficiency, scaling, and energy efficiency.

Main Results:

• Polynomial expansion approaches show potential for reducing computational costs in DFT.
• Comparative analysis reveals performance trade-offs between different expansion methods and traditional diagonalization.
• Performance metrics include accuracy, speed, scalability, and energy consumption on various hardware.

Conclusions:

• Recursive polynomial expansion offers a promising avenue for accelerating large-scale DFT simulations.
• The choice of method depends on specific system sizes and hardware architectures.
• This work contributes to more efficient and scalable quantum mechanical calculations for materials science.