arXiv subjects

Nikhil Kodali

Publications and source records attributed to Nikhil Kodali.

4 recordsLinked to original sources

arXiv2026

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

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 $4\times$--$6.4\times$ 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 $3.4\times$ faster Chebyshev filtering. On Aurora, total self-consistent-field (SCF) solve wall time reduces by $2\times$. An 800-node (9,600-GPU) calculation demonstrates fully relativistic pseudopotential DFT for $\sim$80,000 electrons in under 7 minutes per SCF iteration.

cond-mat.mtrl-sci↗

arXiv2025

Residual-based Chebyshev filtered subspace iteration for sparse Hermitian eigenvalue problems tolerant to inexact matrix-vector products

Chebyshev Filtered Subspace Iteration (ChFSI) is widely used for computing a small subset of extremal eigenpairs from large matrices, particularly when the eigenpairs must be computed repeatedly as the system matrix evolves within an outer nonlinear iteration. In this work, we propose R-ChFSI, a residual-based reformulation that recasts the Chebyshev polynomial recurrence in terms of residuals rather than eigenvector estimates, which achieves robust convergence even when matrix--vector products are computed inexactly. We derive convergence guarantees under such approximations and show that R-ChFSI can naturally leverage (i) the use of inexpensive approximate inverses for generalized eigenproblems of the form $\textbf{A} \textbf{x} = \lambda \textbf{B} \textbf{x}$, where exact factorizations of $\textbf{B}$ are prohibitively expensive, (ii)~low-precision arithmetic (FP32, TF32) for both standard and generalized eigenproblems, and (iii)~reduced-precision (BF16) inter-process communication in distributed sparse matrix--vector products. Controlled experiments on dense random matrices quantitatively verify the convergence bounds derived in this work and confirm the robustness of R-ChFSI to prescribed approximation errors for both standard and generalized eigenproblems. Large-scale experiments on finite-element discretized DFT generalized eigenproblems with up to 85 million grid points and 13,500 eigenpairs demonstrate that R-ChFSI achieves residual norms orders of magnitude below those of standard ChFSI when approximate inverses are employed, and reliably meets target tolerances of $10^{-8}$ even when employing reduced precision, yielding filtering speedups of up to $2.7{\times}$ ($2.1{\times}$ for the full eigensolver) on GPU accelerators

physics.comp-ph↗

arXiv2024

Finite-element methods for noncollinear magnetism and spin-orbit coupling in real-space pseudopotential density functional theory

We introduce an efficient finite-element approach for large-scale real-space pseudopotential density functional theory (DFT) calculations incorporating noncollinear magnetism and spin-orbit coupling. The approach, implemented within the open-source DFT-FE computational framework, fills a significant gap in real-space DFT calculations using finite element basis sets, which offer several advantages over traditional DFT basis sets. In particular, we leverage the local reformulation of DFT electrostatics to derive the finite-element (FE) discretized governing equations involving two-component spinors. We subsequently utilize an efficient self-consistent field iteration approach based on Chebyshev filtered subspace iteration procedure exploiting the sparsity of local and non-local parts of FE discretized Hamiltonian to solve the underlying nonlinear eigenvalue problem based on a two-grid strategy. Furthermore, we propose using a generalized functional within the framework of noncollinear magnetism and spin-orbit coupling with a stationary point at the minima of the Kohn-Sham DFT energy functional to develop a unified framework for computing atomic forces and periodic unit-cell stresses. Validation studies against plane-wave implementations show excellent agreement in ground-state energetics, vertical ionization potentials, magnetic anisotropy energies, band structures, and spin textures. The proposed method achieves up to 8x-11x speed-ups for semi-periodic and non-periodic systems with $\sim$5000-7000 electrons in terms of minimum wall times compared to widely used plane-wave implementations on CPUs in addition to exhibiting significant computational advantage on GPUs.

cond-mat.mtrl-sci↗

arXiv2023

Fast hardware-aware matrix-free algorithm for higher-order finite-element discretized matrix multivector products on distributed systems

Recent hardware-aware matrix-free algorithms for higher-order finite-element (FE) discretized matrix-vector multiplications reduce floating point operations and data access costs compared to traditional sparse matrix approaches. This work proposes efficient matrix-free algorithms for evaluating FE discretized matrix-multivector products on both multi-node CPU and GPU architectures. We address a critical gap in existing matrix-free implementations, which are well suited only for the action of FE discretized matrices on a single vector. We employ batched evaluation strategies, with the batchsize tailored to underlying hardware architectures, leading to better data locality and enabling further parallelization. On CPUs, we utilize even-odd decomposition, SIMD vectorization, and overlapping computation and communication strategies. On GPUs, we employ strategies to overlap compute and data movement in conjunction with GPU shared memory, constant memory, and kernel fusion to reduce data accesses. Our implementation outperforms the baselines for Helmholtz operator action, achieving up to 1.4x improvement on one CPU node and up to 2.8x on one GPU node, while reaching up to 4.4x and 1.5x improvement on multiple nodes for CPUs ($\sim 3000$ cores) and GPUs ($\sim$ 25 GPUs), respectively. We further benchmark the performance of the proposed implementation for solving a model eigenvalue problem for 1024 smallest eigenvalue-eigenvector pairs by employing the Chebyshev Filtered Subspace Iteration method, achieving up to 1.5x improvement on one CPU node and up to 2.2x on one GPU node while reaching up to 3.0x and 1.4x improvement on multinode CPUs ($\sim 3000$ cores) and GPUs ($\sim$ 25 GPUs), respectively.

physics.comp-ph↗