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 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.