arXiv subjects

Kartick Ramakrishnan

Publications and source records attributed to Kartick Ramakrishnan.

6 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↗

arXiv2026

Accelerating finite-element-based projector augmented-wave density functional theory calculations with scalable GPU-centric computational methods

Accurate large-scale Kohn-Sham density functional theory (DFT) calculations are essential for modeling complex material systems, including interfaces, defects, nanoclusters, and twisted two-dimensional heterostructures. Achieving chemical accuracy at scales of $10^4$-$10^5$ electrons with practical time-to-solution, however, remains challenging for existing DFT implementations. We present GPU-centric computational methods and algorithmic innovations within a finite-element (FE) discretized projector augmented-wave (PAW) formulation (PAW-FE) for accurate, efficient, and scalable electronic-structure calculations on modern exascale systems. The FE discretization, developed within a collinear spin formalism, accommodates generic boundary conditions and employs multi-resolution quadrature for accurate evaluation of atom-centered PAW integrals on coarse grids. The resulting generalized Hermitian eigenproblem is solved using residual-based Chebyshev filtered subspace iteration (R-ChFSI). Exploiting R-ChFSI's tolerance to inexact matrix-multivector products, we employ an approximate inverse PAW overlap matrix, mixed-precision arithmetic (FP32/TF32), and low-precision nearest-neighbor communication (BF16) during filtered subspace construction, along with block-wise computation-communication overlap to reduce cost while preserving robustness. These strategies yield up to $8\times$ and $20\times$ CPU-GPU speedups on Intel and AMD GPU architectures, respectively. Compared to plane-wave PAW methods, PAW-FE achieves close to 8$\times$ reduction in time-to-solution for 10,000-electron systems on NVIDIA GPUs, with larger gains at scale, and around 6$\times$ over norm-conserving FE approaches. We demonstrate scalability to 130,000-electron systems, establishing PAW-FE as an exascale-ready method for chemically accurate first-principles simulations.

physics.comp-ph↗

arXiv2026

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 $\textbf{A} \textbf{x} = λ\textbf{B} \textbf{x}$, 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↗

arXiv2025

Real-space methods for ab initio modelling of surfaces and interfaces under external potential bias

Accurate ab initio modelling of surfaces and interfaces, especially under an applied external potential bias, is important for describing and characterizing various phenomena that occur in electronic, catalytic, and energy storage devices. Leveraging the ability of real-space density functional theory (DFT) codes to accommodate generic boundary conditions, we introduce two methods for applying an external potential bias that can be suitable for modelling surfaces and interfaces. In the first method, an external constant electric field is applied by modifying the DFT Hamiltonian via the introduction of an auxiliary linear potential while solving the electrostatic potential arising in DFT using a Poisson equation with zero-Neumann boundary conditions. The second method directly enforces the desired external potential bias by imposing constraints on the electrostatic potential, thereby naturally mimicking experimental conditions. We describe the underlying DFT governing equations for the two setups within the real-space formalism employing finite-element discretization. First, we validate the constant electric field setup within real-space finite-element DFT (DFT-FE) with an equivalent approach using plane-wave DFT (i.e., using periodic boundary conditions) on three representative benchmark systems, namely La-terminated Li$_7$La$_3$Zr$_2$O$_{12}$, GaAs (111), and Al FCC (111) slabs. Subsequently, we present a comprehensive evaluation of the two setups in terms of the average ground-state properties, such as surface and adsorption energies. The methods developed in our work provide an attractive alternative to plane-wave DFT approaches in applying external potential bias that usually suffer from the periodic boundary conditions restrictions and poor scalability on parallel computing architectures.

cond-mat.mtrl-sci↗

arXiv2024

Fast and scalable finite-element based approach for density functional theory calculations using projector-augmented wave method

In this work, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale electronic structure calculations. To the best of our knowledge, this is the first real-space approach for DFT calculations, combining the efficiency of PAW formalism involving smooth electronic fields with the ability of systematically improvable higher-order finite-element basis to achieve significant computational gains. In particular, we have developed efficient strategies for solving the underlying FE discretized PAW generalized eigenproblem by employing the Chebyshev filtered subspace iteration approach to compute the desired eigenspace in each self-consistent field iteration. These strategies leverage the low-rank perturbation of the FE basis overlap matrix in conjunction with reduced order quadrature rules to invert the discretized PAW overlap matrix while also exploiting the sparsity of both the local and non-local parts of the discretized PAW Hamiltonian and overlap matrices. Using the proposed approach, we benchmark the accuracy and performance on various representative examples involving periodic and non-periodic systems with plane-wave-based PAW implementations. Furthermore, we also demonstrate a considerable computational advantage ($\sim$ 5$\times$ -- 10$\times$) over state-of-the-art plane-wave methods for medium to large-scale systems ($\sim$ 6,000 -- 35,000 electrons). Finally, we show that our approach (PAW-FE) significantly reduces the degrees of freedom to achieve the desired accuracy, thereby enabling large-scale DFT simulations ($>$ 50,000 electrons) at an order of magnitude lower computational cost compared to norm-conserving pseudopotential calculations using finite-element discretized calculations.

physics.comp-ph↗

arXiv2023

Chemical bonding in large systems using projected population analysis from real-space density functional theory calculations

We present an efficient and scalable computational approach for conducting projected population analysis from real-space finite-element (FE) based Kohn-Sham density functional theory calculations (DFT-FE). This work provides an important direction towards extracting chemical bonding information from large-scale DFT calculations on materials systems involving thousands of atoms while accommodating periodic, semi-periodic or fully non-periodic boundary conditions. Towards this, we derive the relevant mathematical expressions and develop efficient numerical implementation procedures that are scalable on multi-node CPU architectures to compute the projected overlap and Hamilton populations. The population analysis is accomplished by projecting either the self-consistently converged FE discretized Kohn-Sham orbitals, or the FE discretized Hamiltonian onto a subspace spanned by a localized atom-centred basis set. The proposed methods are implemented in a unified framework within DFT-FE code where the ground-state DFT calculations and the population analysis are performed on the same FE grid. We further benchmark the accuracy and performance of this approach on representative material systems involving periodic and non-periodic DFT calculations with LOBSTER, a widely used projected population analysis code. Finally, we discuss a case study demonstrating the advantages of our scalable approach to extract the quantitative chemical bonding information of hydrogen chemisorbed in large silicon nanoparticles alloyed with carbon, a candidate material for hydrogen storage.

physics.comp-ph↗