标题： 基于ARM和GPU系统的大型尺度有限温度实时时间依赖密度泛函理论计算与混合泛函 显示英文标题

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

摘要： 通过使用混合泛函的实时时间依赖密度泛函理论（rt-TDDFT）计算，可以高保真地模拟起源于有限温度的超快电子现象，例如非线性光学激发。然而，之前使用最佳规范——即并行传输规范——对实际材料进行的rt-TDDFT模拟仅限于低温系统和带隙系统。在本文中，我们引入了并行传输隐式中点（PT-IM）方法，该方法显著加速了具有混合泛函的实际材料的有限温度rt-TDDFT计算。我们首先在我们的平面波代码PWDFT中实现了带有混合泛函的PT-IM，并在GPU和ARM平台上进行了优化，以构建一个坚实的基准代码。接下来，我们提出了一种对角化方法来减少计算和通信复杂度，然后我们采用自适应压缩交换（ACE）方法来减少最昂贵的福克交换算符的频率。最后，我们采用了基于环的方法和共享内存机制，分别重叠计算和通信并减轻内存消耗。数值结果表明，我们优化后的代码可以在192个计算节点上对具有混合泛函的有限温度rt-TDDFT模拟达到3072个原子，单个时间步的求解时间为429.3秒，与基准相比快了41.4倍。 显示英文摘要

摘要： 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.