Large Scale Finite-Temperature Real-time Time Dependent Density Functional Theory Calculation with Hybrid Functional on ARM and GPU Systems

TL;DR

This paper introduces a novel parallel transport-implicit midpoint method and various optimization techniques to significantly accelerate finite-temperature real-time TDDFT calculations with hybrid functionals on ARM and GPU systems, enabling large-scale simulations.

Contribution

The paper presents the PT-IM method and optimization strategies for hybrid functional rt-TDDFT, achieving substantial speedups and enabling simulations of larger systems at finite temperatures.

Findings

Achieved 41.4x speedup over baseline code.

Simulated 3072 atoms in finite-temperature rt-TDDFT.

Reduced computational complexity with new diagonalization and ACE methods.

Abstract

Ultra-fast electronic phenomena originating from finite temperature, such as nonlinear optical excitation, can be simulated with high fidelity via real-time time dependent density functional theory (rt-TDDFT) calculations with hybrid functional. However, previous rt-TDDFT simulations of real materials using the optimal gauge--known as the parallel transport gauge--have been limited to low-temperature systems with band gaps. In this paper, we introduce the parallel transport-implicit midpoint (PT-IM) method, which significantly accelerates finite-temperature rt-TDDFT calculations of real materials with hybrid function. We first implement PT-IM with hybrid functional in our plane wave code PWDFT, and optimized it on both GPU and ARM platforms to build a solid baseline code. Next, we propose a diagonalization method to reduce computation and communication complexity, and then, we employ adaptively compressed exchange (ACE) method to reduce the frequency of the most expensive Fock exchange operator. Finally, we adopt the ring\_based method and the shared memory mechanism to overlap computation and communication and alleviate memory consumption respectively. Numerical results show that our optimized code can reach 3072 atoms for rt-TDDFT simulation with hybrid functional at finite temperature on 192 computing nodes, the time-to-solution for one time step is 429.3s, which is 41.4 times faster compared to the baseline.