BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.4.11//EN TZID:Asia/Kolkata X-WR-TIMEZONE:Asia/Kolkata BEGIN:VEVENT UID:227@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20261104T153000 DTEND;TZID=Asia/Kolkata:20261104T163000 DTSTAMP:20261023T093527Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-defense-finite-element-metho ds-exascale-algorithms-for-fully-relativistic-noncollinear-pseudopotential -density-functional-theory-from-mathematical-formulations-to-efficient-com putation/ SUMMARY:Ph.D Thesis Defense: Finite-element methods & exascale algorithms f or fully relativistic noncollinear pseudopotential density functional theo ry: From mathematical formulations to efficient computationalrealization&m agnetic materials applications DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Def ense\n\n\n\nSpeaker: Mr. NIKHIL KODALI\nS.R. Number: 06-18-01-10-12-21-1-1 9476\nTitle: “Finite-element methods and exascale algorithms for fully r elativistic noncollinear pseudopotential density functional theory: From m athematical formulations to efficient computational realization and magnet ic materials applications”\nResearch Supervisor: Dr. Phani Motamarri\nTh esis examiner : Prof. Gour Prasad Das: Emeritus Professor\, RISE\, TCG Cre st Kolkata\nDate &\; Time : November 04\, 2026 (Wednesday)\, 03:30 PM\n Venue : #102\, CDS Seminar Hall\n\n\n\nABSTRACT\nNext-generation technolog ies such as energy-efficient spintronic memory (MRAM)\, skyrmionic logic d evices\, and topological quantum computing platforms rely on quantum mater ials exhibiting noncollinear (NC) magnetism and spin-orbit coupling (SOC). Predictive first-principles simulations are indispensable for understandi ng and designing these systems\, in which magnetic anisotropy\, spin textu res\, and frustrated magnetic order play a central role. Realistic modelin g of these phenomena in layered magnets and magnetic heterostructures ofte n requires large simulation domains to capture moiré patterns\, defects\, or long-wavelength magnetic textures. However\, performing NC-SOC density functional theory (DFT) calculations efficiently remains challenging\, as they introduce complex two-component spinor wavefunctions\, local and non local spin-dependent Hamiltonian terms\, and significantly larger eigenval ue problems than their collinear counterparts\, making NC-SOC calculations 12x–30x more computationally expensive than unpolarized calculations. T o address these steep computational demands\, this thesis develops exascal e algorithms and mathematical formulations for NC-SOC DFT within a systema tically convergent finite-element (FE) framework. Specifically\, we propos e a local reformulation of DFT electrostatics\, devise a unified force/str ess framework\, develop a residual-based Chebyshev-filtered subspace itera tion (R-ChFSI) eigensolver robust under reduced-precision operations\, and design GPU-optimized data-movement schemes—integrating these advancemen ts into the open-source DFT-FE code. These developments make fully relativ istic calculations for medium-scale systems (~10\,000–20\,000 electrons) highly efficient\, while bringing systematically convergent NC-SOC simula tions of large-scale systems containing up to 100\,000 electrons within re ach for the first time.\n\nWe establish the local real-space formalism for NC-SOC DFT within an FE discretization utilizing optimized norm-conservin g Vanderbilt (ONCV) pseudopotentials. We develop a highly efficient strate gy for the local reformulation of DFT electrostatics to derive the FE-disc retized governing equations involving two-component spinors. To handle exc hange-correlation (XC) effects\, we employ the locally collinear approxima tion and propose robust regularization strategies tailored for FE discreti zation to address numerical singularities in generalized-gradient approxim ation (GGA) functionals in regions of vanishing or small magnetization. Fu rthermore\, we devise a unified generalized force and stress framework to compute accurate atomic forces and periodic unit-cell stresses for NC-SOC systems\, enabling structural relaxation\, unit-cell optimization\, and th e investigation of competing magnetic configurations.\n\nTo address the co mputational bottleneck of solving the resulting sparse generalized eigenva lue problem\, we introduce the residual-based Chebyshev-filtered subspace iteration (R-ChFSI). While traditional ChFSI is suited for repeated eigens olves in self-consistent field (SCF) iterations\, it is highly sensitive t o inexact operations. Consequently\, it fails to converge when using appro ximate inverses of the overlap matrix to construct the Chebyshev-filtered subspace rich in the desired eigenvectors for generalized eigenproblems\, or when leveraging low-precision GPU arithmetic to reduce time-to-solution for the eigensolve. By recasting the Chebyshev polynomial recurrence in t erms of residuals rather than direct eigenvector updates\, we derive a sch eme with provably more robust convergence characteristics under inexact op erations. Consequently\, R-ChFSI achieves robust convergence under approxi mations\, tolerating the use of inexpensive approximate inverses for gener alized eigenproblems\, low-precision arithmetic (FP32/TF32)\, and reduced- precision (BF16) interprocess communication in distributed sparse matrix-v ector products. We demonstrate that R-ChFSI reliably meets stringent elect ronic-structure tolerances (e.g.\, $10^{-8}$ residual tolerance) while pro viding a robust mathematical foundation for leveraging modern GPU hardware .\n\nTo translate these algorithmic advances into high-performance scalabi lity on exascale architectures\, we target key floating-point and data mov ement bottlenecks. Although modern GPU architectures offer dramatically hi gher throughput for low-precision arithmetic\, eigensolvers in scientific simulations have struggled to exploit this capability without sacrificing accuracy. The proposed R-ChFSI algorithm resolves this challenge\, enablin g mixed-precision computations and block floating-point compressed MPI com munication with over 4x compression ratios. Together\, these optimizations dramatically reduce time-to-solution and communication overhead\, enablin g fully relativistic NC-SOC DFT simulations of systems with up to 100\,000 electrons.\n\nWe validate the accuracy\, robustness\, and scaling of our framework through systematic benchmarks and large-scale studies. Eigensolv er benchmarks confirm that R-ChFSI maintains robust convergence under appr oximate inverses and reduced precision\, yielding filtering speedups of up to 2.7x on GPU accelerators compared to standard implementations. By leve raging these eigensolver advances\, the overall FE framework achieves up t o 8x–11x speedups in minimum wall time for semi-periodic and non-periodi c systems with thousands of electrons compared to widely used plane-wave i mplementations on CPUs\, while maintaining excellent agreement in ground-s tate energetics\, forces\, and stresses. Large-scale performance tests dem onstrate excellent strong and weak scalability on modern GPU-accelerated s upercomputers.\n\nTo demonstrate the capability of these developments to e nable novel physical investigations previously computationally inaccessibl e\, we study the layered ferromagnet Fe3GeTe2\, a system of key interest i n 2D magnetism and spintronics. Specifically\, we investigate the role of Fe vacancies\, exploring their impact on the system's energetics\, localiz ed magnetic order near defects\, and defect-defect interactions using full y relativistic\, noncollinear calculations.\n\nFinally\, we present formul ations and results for extending this finite-element approach to curviline ar coordinates. This extension enables the efficient resolution of sharp v ariations in wavefunctions and densities using adaptive\, non-uniform mesh es (leveraging the unique flexibility of finite-element methods)\, thereby reducing the number of degrees of freedom (DoFs) required to achieve a ta rget accuracy. We detail the coordinate transformations of the spinor-valu ed Kohn-Sham equations and electrostatic formulations\, while leveraging t he previously developed generalized force framework to compute forces and stresses. These developments extend systematically convergent\, adaptive r eal-space DFT simulations to curvilinear coordinates.\n\nIn summary\, this work advances both the theoretical formulation and computational realizat ion of relativistic noncollinear DFT\, dramatically accelerating medium-sc ale calculations while enabling systematically convergent simulations at a n unprecedented scale on exascale supercomputers. By developing an FE disc retization for Kohn-Sham DFT utilizing fully relativistic ONCV pseudopoten tials\, formulating a generalized force/stress framework\, designing the R -ChFSI eigensolver\, implementing GPU-centric optimizations\, and extendin g these methods to curvilinear coordinates\, this work provides a robust a nd highly efficient platform for predictive ab initio materials simulation s. These developments effectively bridge the gap between the complex physi cs of relativistic noncollinear magnetic systems and the computational eff iciency required to access experimentally relevant length and time scales. \n\n\n\nALL ARE WELCOME CATEGORIES:Events,Thesis Defense END:VEVENT BEGIN:VTIMEZONE TZID:Asia/Kolkata X-LIC-LOCATION:Asia/Kolkata BEGIN:STANDARD DTSTART:20251104T153000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR