BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Asia/Kolkata X-WR-TIMEZONE:Asia/Kolkata BEGIN:VEVENT UID:154@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20251027T153000 DTEND;TZID=Asia/Kolkata:20251027T163000 DTSTAMP:20251016T124408Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-colloquium-102-cds-27-octobe r-2025-scalable-real-space-finite-element-methods-and-algorithms-for-ab-in itio-material-modelling-in-the-exascale-era-applications-to-energy-materia ls/ SUMMARY:Ph.D: Thesis Colloquium: 102 : CDS: 27\, October 2025 "Scalable rea l-space finite-element methods and algorithms for ab initio material model ling in the exascale era: Applications to energy materials" DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Col loquium\n\n\n\nSpeaker: Mr. Kartick Ramakrishnan\nS.R. Number: 06-18-01-10 -12-20-1-18495\nTitle: "Scalable real-space finite-element methods and alg orithms for ab initio material modelling in the exascale era: Applications to energy materials"\nResearch Supervisor: Dr. Phani Motamarri\nDate & \; Time : October 27\, 2025 (Monday)\, 03:30 PM\nVenue : #102\, CDS Semina r Hall\n\n\n\nABSTRACT\nOver the past six decades\, Kohn-Sham density func tional theory (DFT) has transformed materials research by providing a quan tum mechanical framework for accurate prediction of wide variety of ground -state properties. This predictive capability of DFT has made it ubiquitou s across chemistry\, condensed matter physics\, materials science\, and na noscience\, 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 bee n employed in high-throughput studies to establish structure–property re lationships by screening large materials spaces\, typically involving mate rial systems with only a few hundred atoms. However\, despite rapid advanc es in high-performance computing\, state-of-the-art DFT methods are unable to fully harness emerging exascale architectures\, thereby restricting si mulations to length scales well below tens of nanometres required to captu re collective materials behaviour. Accessing these scales is crucial not o nly 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 lo nger time scales. This thesis seeks to bridge this gap by developing novel real-space computational methodologies and scalable algorithms that are i nherently suited to exascale architectures\, enabling accurate\, robust\, and massively parallel ab initio simulations with a particular focus towar ds their applications to problems in energy storage and catalysis.\n\nTo a ddress these challenges\, this thesis first focuses on the development of a real-space finite-element-based methodology for density functional theor y 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 imp rovable higher-order finite-element (FE) basis to achieve significant comp utational gains across a wide-range of materials systems. Towards this\, w e introduce a local real-space formulation of the PAW energy functional th at is naturally amenable to finite-element discretisation resulting in a l arge-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 numb er of atoms and can exceed 50\,000 in large-scale simulations. The resulti ng eigenproblem is solved using a residual-based Chebyshev filtered subspa ce iteration procedure (R-ChFSI)\, which is inherently tolerant to approxi mations in matrix-vector products. Leveraging this property\, we develop e fficient 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.\n\nFu rthermore\, the robustness of R-ChFSI allows us to develop mixed precision strategies to accelerate computation and communication\, combined with co mpute-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 mate rials systems. We further validate the accuracy and robustness of the prop osed PAW-FE methodology against ABINIT a plane-wave DFT code\, demonstrati ng excellent agreement across representative materials systems.\n\nBuildin g on these developments\, the thesis next presents the formulation of atom ic forces and cell stresses within the PAW-FE framework\, quantities that are essential for structure relaxation and ab initio molecular dynamics si mulations. These correspond to the derivatives of the total energy functio nal with respect to atomic positions and lattice vectors\, respectively. T o this end\, we introduce a new energy functional that has the same statio nary points as the PAW energy functional and employ it to derive an expres sion 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 evaluat ing ionic forces and unit-cell stresses\, while naturally incorporating Pu lay 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 confi rming the conservative nature of the computed forces and stresses.\n\nHavi ng established the accuracy and robustness of our methodology for ground-s tate properties\, we proceed to assess the computational performance and s calability of the proposed methods relative to state-of-the-art (SOTA) DFT approaches. Towards this\, we conduct extensive CPU and GPU benchmarks ag ainst Quantum Espresso (QE)\, a SOTA plane-wave open-source code\, and DFT -FE\, the finite-element framework that was the workhorse behind the ACM G ordon Bell prize winning simulations. These benchmarks are performed on so me of the world’s foremost supercomputing platforms -- ALCF Aurora\, OLC F Frontier\, ALCF Polaris\, and NSM Param Pravega at IISc. We observe more than tenfold reduction in minimum wall time relative to QE for system siz es greater than 8\,000 electrons and more than sixfold reduction in comput ational cost compared to DFT-FE. These results highlight the ability of PA W-FE to efficiently exploit diverse exascale architectures\, exhibiting st rong 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 clust ers\, facilitating the rapid generation of rich datasets for machine-learn ing driven materials modelling.\n\nTo leverage the developed computational algorithms for application problems\, this thesis next introduces a proje cted population analysis methodology to extract quantitative chemical-bond ing information from large-scale real-space finite-element DFT calculation s. Efficient computational strategies are devised to project the finite-el ement–discretized Kohn–Sham orbitals onto atomic orbitals\, enabling t he computation of projected overlap and Hamilton population that character ize bonding interactions between atom pairs. This capability allows chemic al-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 popu lation analysis code\, observing excellent agreement. Finally\, we demonst rate the practical utility of the framework by analysing H₂ chemisorptio n on silicon nanoclusters up to 10 nm in size and investigate the influenc e of carbon alloying on the Si–H bond strength\, showing how carbon allo ying alters local bonding characteristics and influence the thermodynamics of hydrogen adsorption/desorption.\n\nTowards realizing the potential of the developed real-space computational methods for energy storage and cata lysis applications\, the thesis next investigates strategies for accuratel y modelling slabs and surfaces under external potential bias. Exploiting t he capability of real-space methods to accommodate generic boundary condit ions\, 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 elect ric 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 co nditions. Second\, a desired potential bias is imposed directly by constra ining the electrostatic potential in a specified region\, thus allowing th e direct simulation of experimental conditions. We validate the constant-f ield implementation by comparing real-space finite-element DFT results wit h equivalent plane-wave calculations on benchmark systems. Additionally we demonstrate comprehensive evaluation of the two strategies in terms of av erage 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 inter faces under applied bias demonstrating the influence of localized electric fields on interfacial energetics towards the development of design princi ples to optimize interfacial contact between lithium electrodes and solid electrolytes.\n\nIn conclusion\, this thesis advances the boundaries of fi rst-principles materials modelling by developing a new generation of scala ble\, 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 reliabl e simulations of complex materials at unprecedented scales. Together\, the se contributions lay the foundation for predictive\, exascale-ready DFT si mulations that bridge the gap between ab initio theory and real-world mate rials design.\n\n\n\nALL ARE WELCOME CATEGORIES:Events,Ph.D. Thesis Colloquium END:VEVENT BEGIN:VTIMEZONE TZID:Asia/Kolkata X-LIC-LOCATION:Asia/Kolkata BEGIN:STANDARD DTSTART:20241027T153000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR