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Published on: December 18, 2014

Efficient Shift-and-Invert Preconditioning for Multi-GPU Accelerated Density Functional Calculations.

Jeheon Woo¹, Woo Youn Kim¹, Sunghwan Choi²

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

Journal of Chemical Theory and Computation

|August 27, 2024

Summary

This summary is machine-generated.

We developed a new inexact shift-and-invert (ISI) method to speed up electronic structure calculations. This approach enhances eigenvalue convergence and GPU parallelization for faster, large-scale computations.

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Area of Science:

Computational Physics
Quantum Chemistry
Materials Science

Background:

Iterative diagonalization is crucial for electronic structure calculations.
Existing methods face convergence challenges in large-scale systems.
Accelerating these calculations is essential for scientific discovery.

Purpose of the Study:

To introduce a novel inexact shift-and-invert (ISI) preconditioning method.
To enhance the convergence speed of iterative diagonalization.
To improve the parallel efficiency of electronic structure calculations on GPUs.

Main Methods:

Developed an improved ISI preconditioning with optimized shift values.
Utilized a preconditioned conjugate gradient solver for efficient inversion.
Implemented and accelerated the method on state-of-the-art graphical processing units (GPUs).
Assessed performance using real-space density functional calculations for 1D, 2D, and 3D periodic systems.

Main Results:

Achieved significantly faster convergence in iterative diagonalization.
Demonstrated high multi-GPU parallel efficiency.
Enabled single-point density functional calculations for hundreds of atoms in approximately 10 seconds using 8 GPUs.
Validated the method across various system dimensionalities.

Conclusions:

The proposed ISI method accelerates electronic structure calculations.
It offers substantial improvements in both convergence speed and parallel efficiency.
The method is broadly applicable to large-scale diagonalization problems in computational science.