DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations

We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching ~100,000 electrons) using Kohn–Sham density functional theory (DFT). DFT-FE is based on a local real-space variational formulation of the Kohn–Sham DFT energy functional that is discretized using a higher-order adaptive spectral finite-element (FE) basis, and treats pseudopotential and all-electron calculations in the same framework, while accommodating non-periodic, semi-periodic and periodic boundary conditions. We discuss the main aspects of the code, which include, the various strategies of adaptive FE basis generation, and the different approaches employed in the numerical implementation of the solution of the discrete Kohn–Sham problem that are focused on significantly reducing the floating point operations, communication costs and latency. We demonstrate the accuracy of DFT-FE by comparing the energies, ionic forces and periodic cell stresses on a wide range of problems with popularly used DFT codes. Further, we demonstrate that DFT-FE significantly outperforms widely used plane-wave codes—both in CPU-times and wall-times, and on both non-periodic and periodic systems—at systems sizes beyond a few thousand electrons, with over 5-10 fold speedups in systems with more than 10,000 electrons. The benchmark studies also highlight the excellent parallel scalability of DFT-FE, with strong scaling demonstrated on up to 192,000 MPI tasks.我们提出一款精准高效、支持大规模并行的有限元代码DFT-FE，可基于科恩-沈密度泛函理论（Kohn–Sham Density Functional Theory, DFT）开展大规模从头算，最大可处理约100,000个电子的体系。DFT-FE基于科恩-沈DFT能量泛函的局域实空间变分形式，采用高阶自适应谱有限元（Finite Element, FE）基组进行离散化，可在统一框架下同时处理赝势与全电子计算，并支持非周期、半周期及周期边界条件。本文阐述了该代码的核心设计要点，包括自适应FE基组生成的多种策略，以及离散科恩-沈问题数值求解实现中采用的各类优化方法——这些方法旨在显著降低浮点运算量、通信开销与通信延迟。我们通过在大量测试问题上与主流DFT代码对比计算得到的能量、离子力及周期晶胞应力，验证了DFT-FE的计算精度。进一步测试表明，当体系电子数超过数千时，DFT-FE在CPU耗时与墙钟耗时上均显著优于主流平面波代码，且在非周期与周期体系中均表现优异；在电子数超过10,000的体系中，其加速比可达5至10倍以上。基准测试同时验证了DFT-FE优异的并行可扩展性，其强可扩展性已在最多192,000个MPI任务的场景下得到验证。