2.5 Million-Atom Ab Initio Electronic-Structure Simulation of Complex Metallic Heterostructures with DGDFT

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(N
^1.5
) 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.