Million-Atom Ab Initio Electron Dynamics: Discontinuous Galerkin Real-Time Time-Dependent Density Functional Theory

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.