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:200@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20260610T153000
DTEND;TZID=Asia/Kolkata:20260610T163000
DTSTAMP:20260527T063146Z
URL:https://cds.iisc.ac.in/events/ph-dcolloquium102-05june2026finite-eleme
 nt-methods-exascale-algorithms-for-fully-relativistic-noncollinear-pseudop
 otential-density-functional-theory-from-mathematical-formulations-to-effic
 ient/
SUMMARY:Change in Date: Ph.D:Colloquium: Finite-element methods & exascale 
 algorithms for fully relativistic noncollinear pseudopotential density fun
 ctional theory: From mathematical formulations to efficient computational 
 realization & magnetic materials applications
DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Col
 loquium\n\n\n\nSpeaker: Mr. NIKHIL KODALI\nS.R. Number: 06-18-01-10-12-21-
 1-19476\nTitle: “Finite-element methods and exascale algorithms for full
 y relativistic noncollinear pseudopotential density functional theory: Fro
 m mathematical formulations to efficient computational realization and mag
 netic materials applications”\nResearch Supervisor: Dr. Phani Motamarri\
 nDate &amp\; Time : June 10\, 2026 (Wednesday)\, 03:30 PM\nVenue : #102\, 
 CDS Seminar Hall\n\n\n\nABSTRACT\nNext-generation technologies such as ene
 rgy-efficient spintronic memory (MRAM)\, skyrmionic logic devices\, and to
 pological quantum computing platforms rely on quantum materials exhibiting
  noncollinear (NC) magnetism and spin-orbit coupling (SOC). Predictive fir
 st-principles simulations are indispensable for understanding and designin
 g these systems\, in which magnetic anisotropy\, spin textures\, and frust
 rated magnetic order play a central role. Realistic modeling of these phen
 omena in layered magnets and magnetic heterostructures often requires larg
 e simulation domains to capture moiré patterns\, defects\, or long-wavele
 ngth magnetic textures. However\, performing NC-SOC density functional the
 ory (DFT) calculations efficiently remains challenging\, as they introduce
  complex two-component spinor wavefunctions\, local and nonlocal spin-depe
 ndent Hamiltonian terms\, and significantly larger eigenvalue problems tha
 n their collinear counterparts\, making NC-SOC calculations 12x–30x more
  computationally expensive than unpolarized calculations. To address these
  steep computational demands\, this thesis develops exascale algorithms an
 d mathematical formulations for NC-SOC DFT within a systematically converg
 ent finite-element (FE) framework. Specifically\, we propose a local refor
 mulation of DFT electrostatics\, devise a unified force/stress framework\,
  develop a residual-based Chebyshev-filtered subspace iteration (R-ChFSI) 
 eigensolver robust under reduced-precision operations\, and design GPU-opt
 imized data-movement schemes—integrating these advancements into the ope
 n-source DFT-FE code. These developments make fully relativistic calculati
 ons for medium-scale systems (~10\,000–20\,000 electrons) highly efficie
 nt\, while bringing systematically convergent NC-SOC simulations of large-
 scale systems containing up to 100\,000 electrons within reach for the fir
 st time.\n\nWe establish the local real-space formalism for NC-SOC DFT wit
 hin an FE discretization utilizing optimized norm-conserving Vanderbilt (O
 NCV) pseudopotentials. We develop a highly efficient strategy for the loca
 l reformulation of DFT electrostatics to derive the FE-discretized governi
 ng equations involving two-component spinors. To handle exchange-correlati
 on (XC) effects\, we employ the locally collinear approximation and propos
 e robust regularization strategies tailored for FE discretization to addre
 ss numerical singularities in generalized-gradient approximation (GGA) fun
 ctionals in regions of vanishing or small magnetization. Furthermore\, we 
 devise a unified generalized force and stress framework to compute accurat
 e atomic forces and periodic unit-cell stresses for NC-SOC systems\, enabl
 ing structural relaxation\, unit-cell optimization\, and the investigation
  of competing magnetic configurations.\n\nTo address the computational bot
 tleneck of solving the resulting sparse generalized eigenvalue problem\, w
 e introduce the residual-based Chebyshev-filtered subspace iteration (R-Ch
 FSI). While traditional ChFSI is suited for repeated eigensolves in self-c
 onsistent field (SCF) iterations\, it is highly sensitive to inexact opera
 tions. Consequently\, it fails to converge when using approximate inverses
  of the overlap matrix to construct the Chebyshev-filtered subspace rich i
 n the desired eigenvectors for generalized eigenproblems\, or when leverag
 ing low-precision GPU arithmetic to reduce time-to-solution for the eigens
 olve. By recasting the Chebyshev polynomial recurrence in terms of residua
 ls rather than direct eigenvector updates\, we derive a scheme with provab
 ly more robust convergence characteristics under inexact operations. Conse
 quently\, R-ChFSI achieves robust convergence under approximations\, toler
 ating the use of inexpensive approximate inverses for generalized eigenpro
 blems\, low-precision arithmetic (FP32/TF32)\, and reduced-precision (BF16
 ) interprocess communication in distributed sparse matrix-vector products.
  We demonstrate that R-ChFSI reliably meets stringent electronic-structure
  tolerances (e.g.\, $10^{-8}$ residual tolerance) while providing a robust
  mathematical foundation for leveraging modern GPU hardware.\n\nTo transla
 te these algorithmic advances into high-performance scalability on exascal
 e architectures\, we target key floating-point and data movement bottlenec
 ks. Although modern GPU architectures offer dramatically higher throughput
  for low-precision arithmetic\, eigensolvers in scientific simulations hav
 e struggled to exploit this capability without sacrificing accuracy. The p
 roposed R-ChFSI algorithm resolves this challenge\, enabling mixed-precisi
 on computations and block floating-point compressed MPI communication with
  over 4x compression ratios. Together\, these optimizations dramatically r
 educe time-to-solution and communication overhead\, enabling fully relativ
 istic NC-SOC DFT simulations of systems with up to 100\,000 electrons.\n\n
 We validate the accuracy\, robustness\, and scaling of our framework throu
 gh systematic benchmarks and large-scale studies. Eigensolver benchmarks c
 onfirm that R-ChFSI maintains robust convergence under approximate inverse
 s and reduced precision\, yielding filtering speedups of up to 2.7x on GPU
  accelerators compared to standard implementations. By leveraging these ei
 gensolver advances\, the overall FE framework achieves up to 8x–11x spee
 dups in minimum wall time for semi-periodic and non-periodic systems with 
 thousands of electrons compared to widely used plane-wave implementations 
 on CPUs\, while maintaining excellent agreement in ground-state energetics
 \, forces\, and stresses. Large-scale performance tests demonstrate excell
 ent strong and weak scalability on modern GPU-accelerated supercomputers.\
 n\nTo demonstrate the capability of these developments to enable novel phy
 sical investigations previously computationally inaccessible\, we study th
 e layered ferromagnet Fe3GeTe2\, a system of key interest in 2D magnetism 
 and spintronics. Specifically\, we investigate the role of Fe vacancies\, 
 exploring their impact on the system's energetics\, localized magnetic ord
 er near defects\, and defect-defect interactions using fully relativistic\
 , noncollinear calculations.\n\nFinally\, we present formulations and resu
 lts for extending this finite-element approach to curvilinear coordinates.
  This extension enables the efficient resolution of sharp variations in wa
 vefunctions and densities using adaptive\, non-uniform meshes (leveraging 
 the unique flexibility of finite-element methods)\, thereby reducing the n
 umber of degrees of freedom (DoFs) required to achieve a target accuracy. 
 We detail the coordinate transformations of the spinor-valued Kohn-Sham eq
 uations and electrostatic formulations\, while leveraging the previously d
 eveloped generalized force framework to compute forces and stresses. These
  developments extend systematically convergent\, adaptive real-space DFT s
 imulations to curvilinear coordinates.\n\nIn summary\, this work advances 
 both the theoretical formulation and computational realization of relativi
 stic noncollinear DFT\, dramatically accelerating medium-scale calculation
 s while enabling systematically convergent simulations at an unprecedented
  scale on exascale supercomputers. By developing an FE discretization for 
 Kohn-Sham DFT utilizing fully relativistic ONCV pseudopotentials\, formula
 ting a generalized force/stress framework\, designing the R-ChFSI eigensol
 ver\, implementing GPU-centric optimizations\, and extending these methods
  to curvilinear coordinates\, this work provides a robust and highly effic
 ient platform for predictive ab initio materials simulations. These develo
 pments effectively bridge the gap between the complex physics of relativis
 tic noncollinear magnetic systems and the computational efficiency require
 d to access experimentally relevant length and time scales.\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:20250610T153000
TZOFFSETFROM:+0530
TZOFFSETTO:+0530
TZNAME:IST
END:STANDARD
END:VTIMEZONE
END:VCALENDAR