Over the past decades, first-principles real-time time dependent density functional theory(rt-TDDFT) simulations have been limited to systems with only thousands of atoms. We propose a novel method based on the discontinuous Galerkin adaptive local basis, significantly reducing global communication in rt-TDDFT. We further introduce a tensor compression technique that leverages basis locality to avoid repeated evaluation of multi-center integrals in hybrid functionals, greatly reducing computational cost. To overcome the projection bottleneck in our basis sets, we design a fused Gemm-Reduce operation that achieves several times higher floating-point efficiency than standard BLAS combination. Our implementation reaches 34.8% of theoretical peak performance on 524,288 CGs of the New Sunway supercomputer and simulates electronic dynamics of systems with over one million atoms for both local-semi-local and hybrid functionals. This work improves computational scale by two orders of magnitude, opening new possibilities for exploring ultrafast dynamics in large-scale materials and nanophotonic devices.

First-principles density functional theory (DFT) with plane wave (PW) basis set is the most widely used method in quantum mechanical material simulations due to its advantages in accuracy and universality. However, a perceived drawback of PW-based DFT calculations is their substantial computational cost and memory usage, which currently limits their ability to simulate large-scale complex systems containing thousands of atoms. This situation is exacerbated in the new Sunway supercomputer, where each process is limited to a mere 16 GB of memory. Herein, we present a novel parallel implementation of plane wave density functional theory on the new Sunway supercomputer (PWDFT-SW). PWDFT-SW fully extracts the benefits of Sunway supercomputer by extensively refactoring and calibrating our algorithms to align with the system characteristics of the Sunway system. Through extensive numerical experiments, we demonstrate that our methods can substantially decrease both computational costs and memory usage. Our optimizations translate to a speedup of 64.8x for a physical system containing 4,096 silicon atoms, enabling us to push the limit of PW-based DFT calculations to large-scale systems containing 16,384 carbon atoms.

Raman spectroscopy offers invaluable insights into the chemical composition and structural characteristics of various materials, making it a powerful tool for structural analysis. However, accurate quantum mechanical simulations of Raman spectra for large systems, such as biological materials, have been limited due to immense computational costs and technical challenges. In this study, we developed efficient algorithms and optimized implementations on heterogeneous computing architectures to enable fast and highly scalable ab initio simulations of Raman spectra for large-scale biological systems with up to 100 million atoms. Our simulations have achieved nearly linear strong and weak scaling on two cutting-edge high-performance computing systems, with peak FP64 performances reaching 400 PFLOPS on 96,000 nodes of new Sunway supercomputer and 85 PFLOPS on 6,000 node of ORISE supercomputer. These advances provide promising prospects for extending quantum mechanical simulations to biological systems.

GW approximation is a powerful approach to accurately describe the excited-state of semiconductors. However, GW incurs high computational cost $\mathcal{O}\left(N^{4}\right)$ and large memory usage $\mathcal{O}\left(N^{3}\right)$, limiting its applications to thousands of (2,742) atoms even on leadership supercomputers. Herein we present a massively parallel implementation of accurate and efficient cubic-scaling plane-wave GW calculations by using low-rank approximations and high-performance computing on leadership supercomputers. By using a series of low rank approximations, we can reduce the expensive GW calculations to the cubic-scaling computational cost $\mathcal{O}\left(N^{3}\right)$ and quadratic memory usage $\mathcal{O}\left(N^{2}\right)$. With the help of parallel and communication optimization, the plane-wave GW calculations gain an overall speedup of over 70x and efficiently scale up to 13,824 atoms within a few minutes using 449,280 cores on new Sunway supercomputer. This accomplishment paves the way for excited-state quantum mechanical material simulations at mesoscopic scale (10K atoms) and for the design of next-generation semiconductor devices.

First-principles time-dependent density functional theory (TDDFT) is a powerful tool to accurately describe the excited-state properties of molecules and solids in condensed matter physics , computational chemistry, and materials science. However, a perceived drawback in TDDFT calculations is its ultrahigh computational cost O ( N 5 ∼ N 6 ) and large memory usage O ( N 4 ) especially for plane-wave basis set, confining its applications to large systems containing thousands of atoms. Here, we present a massively parallel implementation of linear-response TDDFT (LR-TDDFT) and accelerate LR-TDDFT in two different aspects: (1) numerical algorithms on the X86 supercomputer and (2) optimizations on the heterogeneous architecture of the new Sunway supercomputer. Furthermore, we carefully design the parallel data and task distribution schemes to accommodate the physical nature of different computation steps. By utilizing these two different methods, our implementation can gain an overall speedup of 10x and 80x and efficiently scales to large systems up to 4096 and 2744 atoms within dozens of seconds.

First-principles time-dependent density functional theory (TDDFT) is a powerful tool to accurately describe the excited-state properties of molecules and solids in condensed matter physics, computational chemistry and materials science. However, a perceived drawback in TDDFT calculations is its ultrahigh computational cost and large memory usage especially for plane-wave basis set, confining its applications to large systems containing thousands of atoms. Here, we present a massively parallel implementation of linear-response TDDFT (LR-TDDFT) and reduce the complexity to by combining K-Means clustering based low-rank approximation with iterative eigensolve algorithm. Furthermore, we carefully design the parallel data and task distribution schemes to accommodate with the physical nature in different steps of the computation, also, several optimization methods are employed to effectively handle the matrix operations and data communications of constructing and diagonalizing the LR-TDDFT Hamiltonian. In particular, our method can significantly reduce the cost of computation and memory by nearly 2 orders of magnitude compared to conventional LR-TDDFT calculations. Numerical results demonstrate that our implementation can gain an overall speedup of 10x and efficiently scale up to 12,288 CPU cores for large systems up to 4,096 atoms within dozens of seconds.

Over the past three decades, ab initio electronic structure calculations of large, complex and metallic systems are limited to tens of thousands of atoms in computational accuracy and efficiency on leadership supercomputers. We present a massively parallel discontinuous Galerkin density functional theory (DGDFT) implementation, which adopts adaptive local basis functions to discretize the Kohn-Sham equation, resulting in a block-sparse Hamiltonian matrix. A highly efficient pole expansion and selected inversion (PEXSI) sparse direct solver is implemented in DGDFT to achieve O(N1.5) scaling for quasi two-dimensional systems. DGDFT allows us to compute the electronic structures of complex metallic heterostructures with 2.5 million atoms (17.2 million electrons) using 35.9 million cores on the new Sunway supercomputer. The peak performance of PEXSI can achieve 64 PFLOPS (~5% of theoretical peak), which is un-precedented for sparse direct solvers. This accomplishment paves the way for quantum mechanical simulations into mesoscopic scale for designing next-generation electronic devices.