Massively parallel GPU-accelerated minimization of classical density functional theory.

Area of Science:

• Computational physics
• Statistical mechanics
• Materials science

Background:

• Classical density functional theory (DFT) and fundamental measure theory (FMT) are key for understanding systems of hard particles.
• Numerical minimization of the grand potential is computationally intensive, especially in higher dimensions.

Purpose of the Study:

• To explore the numerical minimization of the grand potential for hard disks (2D) and hard spheres (3D).
• To evaluate the performance of massively parallel computations on modern graphics cards for these minimization problems.

Main Methods:

• Implementation of grand potential minimization algorithms on graphics processing units (GPUs).
• Comparison of massively parallel minimization schemes with standard sequential methods.
• Application of classical density functional theory and fundamental measure theory.

Main Results:

• Massively parallel minimization demonstrates significant performance gains over sequential schemes.
• The parallel approach drastically reduces computational time for grand potential minimization.
• Accuracy and computational cost are effectively balanced in complex scenarios using heavy parallelization.

Conclusions:

• Massively parallel minimization on GPUs offers a substantial performance advantage for hard particle systems.
• This computational strategy is crucial for efficient and accurate simulations in complex, multi-dimensional systems.
• The findings pave the way for more extensive studies in statistical mechanics and materials science.