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Dynamic Precision Approach for Accelerating Large-Scale Eigenvalue Solvers in Electronic Structure Calculations on

Jeheon Woo¹, Seonghwan Kim¹, Woo Youn Kim¹

¹Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea.

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Summary

This summary is machine-generated.

This study introduces a dynamic precision method to speed up electronic structure calculations on GPUs. By intelligently switching between single, double, and mixed precision, it achieves significant acceleration while maintaining accuracy.

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Area of Science:

Computational physics
Materials science
Quantum chemistry

Background:

Single precision (SP) arithmetic offers significant speedups on GPUs compared to double precision (DP).
However, using SP exclusively in electronic structure calculations compromises the required accuracy.
Accelerating these calculations is crucial for large-scale simulations.

Purpose of the Study:

To develop a dynamic precision approach for accelerating electronic structure calculations on GPUs.
To maintain the accuracy of double precision (DP) while leveraging the speed of single precision (SP).
To apply this method to accelerate large-scale eigenvalue solvers for Kohn-Sham equations.

Main Methods:

Implemented a 3-fold dynamic precision switching strategy (SP, DP, mixed precision) within an iterative diagonalization process.
Applied the dynamic precision approach to the locally optimal block preconditioned conjugate gradient method.
Determined optimal precision switching thresholds by analyzing convergence patterns using the kinetic energy operator of the Kohn-Sham Hamiltonian.

Main Results:

Achieved speedups of up to 8.53x for band structure calculations.
Achieved speedups of up to 6.60x for self-consistent field (SCF) calculations.
Demonstrated effectiveness across various test systems and boundary conditions on NVIDIA GPUs.

Conclusions:

The proposed 3-fold dynamic precision approach effectively accelerates electronic structure calculations on GPUs.
This method successfully balances computational speed with the accuracy requirements of DP.
Significant performance gains are achievable for large-scale quantum mechanical simulations.