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UID:227@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20261130T153000
DTEND;TZID=Asia/Kolkata:20261130T163000
DTSTAMP:20260915T163936Z
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 &amp\; Time : November 30\, 2026 (Monday)\, 03:30 PM\nVen
 ue : #102\, CDS Seminar Hall\n\n\n\nABSTRACT\nNext-generation technologies
  such as energy-efficient spintronic memory (MRAM)\, skyrmionic logic devi
 ces\, and topological quantum computing platforms rely on quantum material
 s exhibiting noncollinear (NC) magnetism and spin-orbit coupling (SOC). Pr
 edictive first-principles simulations are indispensable for understanding 
 and designing these systems\, in which magnetic anisotropy\, spin textures
 \, and frustrated magnetic order play a central role. Realistic modeling o
 f these phenomena in layered magnets and magnetic heterostructures often r
 equires large simulation domains to capture moiré patterns\, defects\, or
  long-wavelength magnetic textures. However\, performing NC-SOC density fu
 nctional theory (DFT) calculations efficiently remains challenging\, as th
 ey introduce complex two-component spinor wavefunctions\, local and nonloc
 al spin-dependent Hamiltonian terms\, and significantly larger eigenvalue 
 problems than their collinear counterparts\, making NC-SOC calculations 12
 x–30x more computationally expensive than unpolarized calculations. To a
 ddress these steep computational demands\, this thesis develops exascale a
 lgorithms and mathematical formulations for NC-SOC DFT within a systematic
 ally convergent finite-element (FE) framework. Specifically\, we propose a
  local reformulation of DFT electrostatics\, devise a unified force/stress
  framework\, develop a residual-based Chebyshev-filtered subspace iteratio
 n (R-ChFSI) eigensolver robust under reduced-precision operations\, and de
 sign GPU-optimized data-movement schemes—integrating these advancements 
 into the open-source DFT-FE code. These developments make fully relativist
 ic calculations for medium-scale systems (~10\,000–20\,000 electrons) hi
 ghly efficient\, while bringing systematically convergent NC-SOC simulatio
 ns of large-scale systems containing up to 100\,000 electrons within reach
  for the first time.\n\nWe establish the local real-space formalism for NC
 -SOC DFT within an FE discretization utilizing optimized norm-conserving V
 anderbilt (ONCV) pseudopotentials. We develop a highly efficient strategy 
 for the local reformulation of DFT electrostatics to derive the FE-discret
 ized governing equations involving two-component spinors. To handle exchan
 ge-correlation (XC) effects\, we employ the locally collinear approximatio
 n and propose robust regularization strategies tailored for FE discretizat
 ion to address numerical singularities in generalized-gradient approximati
 on (GGA) functionals in regions of vanishing or small magnetization. Furth
 ermore\, we devise a unified generalized force and stress framework to com
 pute accurate atomic forces and periodic unit-cell stresses for NC-SOC sys
 tems\, enabling structural relaxation\, unit-cell optimization\, and the i
 nvestigation of competing magnetic configurations.\n\nTo address the compu
 tational bottleneck of solving the resulting sparse generalized eigenvalue
  problem\, we introduce the residual-based Chebyshev-filtered subspace ite
 ration (R-ChFSI). While traditional ChFSI is suited for repeated eigensolv
 es in self-consistent field (SCF) iterations\, it is highly sensitive to i
 nexact operations. Consequently\, it fails to converge when using approxim
 ate inverses of the overlap matrix to construct the Chebyshev-filtered sub
 space rich in the desired eigenvectors for generalized eigenproblems\, or 
 when leveraging low-precision GPU arithmetic to reduce time-to-solution fo
 r the eigensolve. By recasting the Chebyshev polynomial recurrence in term
 s of residuals rather than direct eigenvector updates\, we derive a scheme
  with provably more robust convergence characteristics under inexact opera
 tions. Consequently\, R-ChFSI achieves robust convergence under approximat
 ions\, tolerating the use of inexpensive approximate inverses for generali
 zed eigenproblems\, low-precision arithmetic (FP32/TF32)\, and reduced-pre
 cision (BF16) interprocess communication in distributed sparse matrix-vect
 or products. We demonstrate that R-ChFSI reliably meets stringent electron
 ic-structure tolerances (e.g.\, $10^{-8}$ residual tolerance) while provid
 ing a robust mathematical foundation for leveraging modern GPU hardware.\n
 \nTo translate these algorithmic advances into high-performance scalabilit
 y on exascale architectures\, we target key floating-point and data moveme
 nt bottlenecks. Although modern GPU architectures offer dramatically highe
 r throughput for low-precision arithmetic\, eigensolvers in scientific sim
 ulations have struggled to exploit this capability without sacrificing acc
 uracy. The proposed R-ChFSI algorithm resolves this challenge\, enabling m
 ixed-precision computations and block floating-point compressed MPI commun
 ication with over 4x compression ratios. Together\, these optimizations dr
 amatically reduce time-to-solution and communication overhead\, enabling f
 ully relativistic NC-SOC DFT simulations of systems with up to 100\,000 el
 ectrons.\n\nWe validate the accuracy\, robustness\, and scaling of our fra
 mework through systematic benchmarks and large-scale studies. Eigensolver 
 benchmarks confirm that R-ChFSI maintains robust convergence under approxi
 mate inverses and reduced precision\, yielding filtering speedups of up to
  2.7x on GPU accelerators compared to standard implementations. By leverag
 ing these eigensolver advances\, the overall FE framework achieves up to 8
 x–11x speedups in minimum wall time for semi-periodic and non-periodic s
 ystems with thousands of electrons compared to widely used plane-wave impl
 ementations on CPUs\, while maintaining excellent agreement in ground-stat
 e energetics\, forces\, and stresses. Large-scale performance tests demons
 trate excellent strong and weak scalability on modern GPU-accelerated supe
 rcomputers.\n\nTo demonstrate the capability of these developments to enab
 le novel physical investigations previously computationally inaccessible\,
  we study the layered ferromagnet Fe3GeTe2\, a system of key interest in 2
 D magnetism and spintronics. Specifically\, we investigate the role of Fe 
 vacancies\, exploring their impact on the system's energetics\, localized 
 magnetic order near defects\, and defect-defect interactions using fully r
 elativistic\, noncollinear calculations.\n\nFinally\, we present formulati
 ons and results for extending this finite-element approach to curvilinear 
 coordinates. This extension enables the efficient resolution of sharp vari
 ations in wavefunctions and densities using adaptive\, non-uniform meshes 
 (leveraging the unique flexibility of finite-element methods)\, thereby re
 ducing the number of degrees of freedom (DoFs) required to achieve a targe
 t accuracy. We detail the coordinate transformations of the spinor-valued 
 Kohn-Sham equations and electrostatic formulations\, while leveraging the 
 previously developed generalized force framework to compute forces and str
 esses. These developments extend systematically convergent\, adaptive real
 -space DFT simulations to curvilinear coordinates.\n\nIn summary\, this wo
 rk advances both the theoretical formulation and computational realization
  of relativistic noncollinear DFT\, dramatically accelerating medium-scale
  calculations while enabling systematically convergent simulations at an u
 nprecedented scale on exascale supercomputers. By developing an FE discret
 ization for Kohn-Sham DFT utilizing fully relativistic ONCV pseudopotentia
 ls\, formulating a generalized force/stress framework\, designing the R-Ch
 FSI eigensolver\, implementing GPU-centric optimizations\, and extending t
 hese methods to curvilinear coordinates\, this work provides a robust and 
 highly efficient platform for predictive ab initio materials simulations. 
 These developments effectively bridge the gap between the complex physics 
 of relativistic noncollinear magnetic systems and the computational effici
 ency required to access experimentally relevant length and time scales.\n\
 n\n\nALL ARE WELCOME
CATEGORIES:Events,Thesis Defense
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