Modern GPU supercomputers offer far higher throughput for low-precision arithmetic than for double precision, and moving data between devices is often more expensive than computing on it. Eigensolvers in scientific simulations have struggled to exploit either fact without losing accuracy. Building on the robustness of the R-ChFSI eigensolver, this project develops a GPU-centric, exascale-oriented finite-element DFT framework for noncollinear magnetism and spin-orbit coupling that targets both floating-point and data-movement bottlenecks.
The framework combines:
adaptive higher-order finite-element discretization and a matrix-free Poisson solver;
GPU-optimized Hamiltonian-multivector products for two-component spinors;
mixed-precision filtering, with cell-level products in FP32/TF32 while residuals are kept in FP64;
block floating-point (BFP) compression of the nearest-neighbour halo data exchanged between MPI ranks;
communication-efficient band parallelization and a distributed blockwise Rayleigh-Ritz procedure.
Together these techniques make systematically convergent, fully relativistic DFT calculations on systems with tens of thousands of electrons practical on leadership-class machines such as Aurora and Frontier. This work has been accepted at SC26.
The finite-element mesh is partitioned across GPUs; the halo data exchanged between neighbouring partitions is compressed to a block floating-point format before communication and decompressed on arrival.
References
2026
SC26
Towards exascale fully relativistic pseudopotential density functional theory calculations enabled by mixed-precision computation and compressed-communication using residual based subspace iteration
Nikhil Kodali, Gourab Panigrahi, Nishant Gupta, and 6 more authors
In The International Conference for High Performance Computing, Networking, Storage, and Analysis (SC26), 2026
Materials exhibiting noncollinear magnetism or strong spin-orbit-coupling underpin many spintronic and topological applications, but their simulations require complex two-component spinors and costs substantially more than scalar density functional theory (DFT). We present a GPU-centric exascale finite-element DFT framework with noncollinear magnetism and spin-orbit-coupling, combining (i) adaptive higher-order finite-element discretization, (ii) a matrix-free Poisson solver, (iii) residual-based Chebyshev filtered subspace iteration (R-ChFSI) for sparse generalized eigenproblems, (iv) R-ChFSI-enabled mixed precision computation with block floating-point compressed MPI communication, and (v) communication-efficient band partitioning. R-ChFSI permits inexact matrix-multivector products and 4x–6.4x compression of communicated data relative to FP64 while preserving double-precision robustness and reducing computation and data movement. Results demonstrate strong scaling on Aurora and Frontier, with up to 3.4x faster Chebyshev filtering. On Aurora, total self-consistent-field (SCF) solve wall time reduces by 2x. An 800-node (9,600-GPU) calculation demonstrates fully relativistic pseudopotential DFT for 80,000 electrons in under 7 minutes per SCF iteration.
@inproceedings{kodali2026exascalencsoc,title={Towards exascale fully relativistic pseudopotential density functional theory calculations enabled by mixed-precision computation and compressed-communication using residual based subspace iteration},author={Kodali, Nikhil and Panigrahi, Gourab and Gupta, Nishant and Ramakrishnan, Kartick and G, Sundaresan and Panch, Rudra and Das, Sambit and Rao, Vishwas and Motamarri, Phani},booktitle={The International Conference for High Performance Computing, Networking, Storage, and Analysis (SC26)},year={2026},note={Accepted},url={https://arxiv.org/abs/2605.30128},ownpub={true}}
