Towards exascale fully relativistic pseudopotential density functional theory calculations enabled by mixed-precision computation and compressed-communication using residual based subspace iteration

Abstract: Noncollinear (NC) magnetism and spin-orbit coupling (SOC) are indispensable for predictive ab initio materials simulations with pronounced relativistic effects and magnetic frustration, yet they significantly increase the cost of cubic-scaling density functional theory (DFT) by introducing complex 2-component wavefunctions per electron and consequently much larger eigenproblems. We present a GPU-centric high-performance framework for NC-SOC DFT that combines: (i) algorithmic advances for solving finite-element (FE) discretized DFT equations; (ii) residual-based Chebyshev filtered subspace iteration (R-ChFSI), tolerant to inexact matrix-vector products, for the resulting sparse generalized eigenproblem; (iii) a matrix-free strategy for accelerating FE Poisson solver; (iv) R-ChFSI-enabled mixed-precision computation with block floating-point compressed MPI communication at compression ratios over 4x, preserving double-precision robustness while reducing compute and data movement costs; and (v) a communication efficient band-partitioning algorithm to improve scalability. Numerical results demonstrate improved time-to-solution and excellent scaling on exascale architectures, enabling fully relativistic pseudopotential DFT simulations of up to 100,000 electrons.