DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES
Ph.D. Thesis Colloquium
Speaker: Mr. Kartick Ramakrishnan
S.R. Number: 06-18-01-10-12-20-1-18495
Title: “Scalable real-space finite-element methods and algorithms for ab initio material modelling in the exascale era: Applications to energy materials”
Research Supervisor: Dr. Phani Motamarri
Date & Time : October 27, 2025 (Monday), 03:30 PM
Venue : #102, CDS Seminar Hall
ABSTRACT
Over the past six decades, Kohn-Sham density functional theory (DFT) has transformed materials research by providing a quantum mechanical framework for accurate prediction of wide variety of ground-state properties. This predictive capability of DFT has made it ubiquitous across chemistry, condensed matter physics, materials science, and nanoscience, powering discoveries in catalysis, energy conversion, light-weight alloys, electronic materials, while consuming 30-40% of the world’s high performance computing resources today. Traditionally, DFT has been employed in high-throughput studies to establish structure–property relationships by screening large materials spaces, typically involving material systems with only a few hundred atoms. However, despite rapid advances in high-performance computing, state-of-the-art DFT methods are unable to fully harness emerging exascale architectures, thereby restricting simulations to length scales well below tens of nanometres required to capture collective materials behaviour. Accessing these scales is crucial not only for understanding complex phenomena in realistic materials systems but also for generating rich, high-fidelity datasets that can drive machine-learning models towards predictive simulations across larger length and longer time scales. This thesis seeks to bridge this gap by developing novel real-space computational methodologies and scalable algorithms that are inherently suited to exascale architectures, enabling accurate, robust, and massively parallel ab initio simulations with a particular focus towards their applications to problems in energy storage and catalysis.
To address these challenges, this thesis first focuses on the development of a real-space finite-element-based methodology for density functional theory within the projector augmented-wave (PAW) formalism, hereafter referred to as PAW-FE. 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 (FE) basis to achieve significant computational gains across a wide-range of materials systems. Towards this, we introduce a local real-space formulation of the PAW energy functional that is naturally amenable to finite-element discretisation resulting in a large-sparse generalised eigenvalue problem (GHEP). A central computational challenge in PAW-FE lies in efficiently computing the lowest N eigenpairs of this large, sparse eigenproblem, where N is proportional to the number of atoms and can exceed 50,000 in large-scale simulations. The resulting eigenproblem is solved using a residual-based Chebyshev filtered subspace iteration procedure (R-ChFSI), which is inherently tolerant to approximations in matrix-vector products. Leveraging this property, we develop efficient strategies that exploit the low-rank perturbation of the FE basis overlap matrix together with the reduced order quadrature rules to invert the discretised PAW overlap matrix, while utilizing the sparsity of both the local and nonlocal parts of the resulting discretised matrices.
Furthermore, the robustness of R-ChFSI allows us to develop mixed precision strategies to accelerate computation and communication, combined with compute-communication overlap techniques that yield substantial performance gains on modern GPU architectures without compromising accuracy. Together, these advances enable scalable simulations of medium to large-scale materials systems. We further validate the accuracy and robustness of the proposed PAW-FE methodology against ABINIT a plane-wave DFT code, demonstrating excellent agreement across representative materials systems.
Building on these developments, the thesis next presents the formulation of atomic forces and cell stresses within the PAW-FE framework, quantities that are essential for structure relaxation and ab initio molecular dynamics simulations. These correspond to the derivatives of the total energy functional with respect to atomic positions and lattice vectors, respectively. To this end, we introduce a new energy functional that has the same stationary points as the PAW energy functional and employ it to derive an expression for the generalised force as a directional derivative of this energy functional with respect to a parameter that perturbs the underlying space. Consequently, this formulation provides a unified expression for evaluating ionic forces and unit-cell stresses, while naturally incorporating Pulay contributions. The resulting formulation is agnostic to the underlying discretisation scheme employed, making it broadly applicable across real-space methods. We validate this approach within the PAW-FE formulation by benchmarking against ABINIT, demonstrating excellent agreement and confirming the conservative nature of the computed forces and stresses.
Having established the accuracy and robustness of our methodology for ground-state properties, we proceed to assess the computational performance and scalability of the proposed methods relative to state-of-the-art (SOTA) DFT approaches. Towards this, we conduct extensive CPU and GPU benchmarks against Quantum Espresso (QE), a SOTA plane-wave open-source code, and DFT-FE, the finite-element framework that was the workhorse behind the ACM Gordon Bell prize winning simulations. These benchmarks are performed on some of the world’s foremost supercomputing platforms — ALCF Aurora, OLCF Frontier, ALCF Polaris, and NSM Param Pravega at IISc. We observe more than tenfold reduction in minimum wall time relative to QE for system sizes greater than 8,000 electrons and more than sixfold reduction in computational cost compared to DFT-FE. These results highlight the ability of PAW-FE to efficiently exploit diverse exascale architectures, exhibiting strong parallel scalability and performance portability across heterogeneous computing environments. Furthermore, the computational efficiency of our approach enables high-fidelity simulations on modest, in-house GPU clusters, facilitating the rapid generation of rich datasets for machine-learning driven materials modelling.
To leverage the developed computational algorithms for application problems, this thesis next introduces a projected population analysis methodology to extract quantitative chemical-bonding information from large-scale real-space finite-element DFT calculations. Efficient computational strategies are devised to project the finite-element–discretized Kohn–Sham orbitals onto atomic orbitals, enabling the computation of projected overlap and Hamilton population that characterize bonding interactions between atom pairs. This capability allows chemical-bonding analyses for systems containing thousands of atoms well beyond the reach of traditional plane-wave approaches. We benchmark the accuracy and performance of our implementation against LOBSTER, a widely used population analysis code, observing excellent agreement. Finally, we demonstrate the practical utility of the framework by analysing H₂ chemisorption on silicon nanoclusters up to 10 nm in size and investigate the influence of carbon alloying on the Si–H bond strength, showing how carbon alloying alters local bonding characteristics and influence the thermodynamics of hydrogen adsorption/desorption.
Towards realizing the potential of the developed real-space computational methods for energy storage and catalysis applications, the thesis next investigates strategies for accurately modelling slabs and surfaces under external potential bias. Exploiting the capability of real-space methods to accommodate generic boundary conditions, a generalized framework for applying external bias across surfaces and interfaces within finite-element DFT is established. Two complementary strategies are devised in this regard. First, an external constant electric field is introduced by modifying the DFT Hamiltonian with an auxiliary linear potential, while the electrostatic potential involved in the DFT problem is solved through a Poisson equation with zero-Neumann boundary conditions. Second, a desired potential bias is imposed directly by constraining the electrostatic potential in a specified region, thus allowing the direct simulation of experimental conditions. We validate the constant-field implementation by comparing real-space finite-element DFT results with equivalent plane-wave calculations on benchmark systems. Additionally we demonstrate comprehensive evaluation of the two strategies in terms of average ground-state properties such as surface and adsorption energies as a function of external potential bias. Finally, using this framework, we present initial simulations of lithium wetting at solid||electrolyte interfaces under applied bias demonstrating the influence of localized electric fields on interfacial energetics towards the development of design principles to optimize interfacial contact between lithium electrodes and solid electrolytes.
In conclusion, this thesis advances the boundaries of first-principles materials modelling by developing a new generation of scalable, real-space computational methods capable of harnessing the power of emerging exascale architectures. The research introduces formulations and algorithms that are accurate, efficient, and scalable—enabling reliable simulations of complex materials at unprecedented scales. Together, these contributions lay the foundation for predictive, exascale-ready DFT simulations that bridge the gap between ab initio theory and real-world materials design.
ALL ARE WELCOME
