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.

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.

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.