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:64@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20240805T150000 DTEND;TZID=Asia/Kolkata:20240805T160000 DTSTAMP:20240716T030555Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-defense-cds-05-august-2024-a -scalable-asynchronous-discontinuous-galerkin-method-for-massively-paralle l-flow-simulations/ SUMMARY:Ph.D. Thesis Defense: CDS: 05\, August 2024 "A scalable asynchronou s discontinuous Galerkin method for massively parallel flow simulations" DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Def ense\n\n\n\nSpeaker : Mr. Shubham Kumar Goswami\nS.R. Number : 06-18-00-10 -12-19-1-17224\nTitle : "A scalable asynchronous discontinuous Galerkin me thod for massively parallel flow simulations "\nThesis examiner: Dr. Prave en Chandrashekar\, Center for Applicable Mathematics Tata Institute of Fun damental Research.\nResearch Supervisor: Dr. Konduri Aditya\nDate &\; T ime : August 05\, 2024 (Monday) at 03:00 PM\nVenue : # 102 CDS Seminar Hal l\n\n\n\nABSTRACT\n\nAccurate simulations of turbulent flows are crucial f or understanding numerous complex phenomena in engineered systems and natu ral processes. Notably\, under realistic conditions with high Reynolds num bers and complex geometries\, the partial differential equations (PDEs) go verning these fluid flows are highly nonlinear and are solved numerically using PDE solvers. Due to the presence of multiple length and time scales inherent to turbulent flows\, these simulations are often computationally expensive\, necessitating the use of massively parallel supercomputers. De spite several advancements in the development of scalable PDE solvers\, th ey face scalability challenges at extreme scales due to communication over head. To address this issue\, an asynchronous computing approach that rela xes communication/synchronization at a mathematical level has been develop ed with finite difference schemes. However\, these schemes are not amenabl e to capture flows in complex geometries with unstructured meshes. The obj ective of this thesis is to develop an asynchronous discontinuous Galerkin (ADG) method with the potential to provide high-order accurate solutions for various flow problems on structured and unstructured meshes and demons trate its scalability. The thesis includes developing an approach to coupl e asynchronous schemes with low-storage Runge-Kutta schemes\, then introdu cing the ADG method and investigating its properties\, and finally impleme nting the proposed method into deal.II (open-source library) for scalabili ty demonstrations.\n\nBased on the asynchronous computing approach\, sever al PDE solvers have been developed that use high-order asynchrony-tolerant (AT) finite difference schemes for spatial discretization to simulate rea cting and non-reacting turbulent flows\, achieving significant improvement s in scalability. For time integration\, they use either multi-step Adams- Bashforth schemes\, which possess poor stability\, or multi-stage Runge-Ku tta (RK) schemes with an over-decomposed domain that necessitates larger m essage sizes for communication and redundant computations. In this work\, we propose a novel method to couple asynchrony-tolerant and low-storage ex plicit RK (LSERK) schemes to solve time-dependent PDEs with reduced commun ication efforts. We develop new schemes for ghost or buffer point updates that are necessary to maintain the desired order of accuracy. The accuracy of this method has been investigated both theoretically and numerically u sing simple one-dimensional linear model equations. Thereafter\, we demons trate its scalability through three-dimensional simulations of decaying Bu rgers’ turbulence performed using two different asynchronous algorithms: communication-avoiding and synchronization-avoiding algorithms. Scalabili ty studies up to 27\,000 cores yielded a speed-up of up to 6x compared to a baseline synchronous algorithm.\n\nIn recent years\, the discontinuous G alerkin (DG) method has gained considerable attention in developing PDE so lvers\, particularly for nonlinear hyperbolic problems\, due to its abilit y to provide high-order accurate solutions in complex geometries\, capture discontinuities\, and exhibit high arithmetic intensity. However\, the sc alability of DG-based solvers is hindered by communication bottlenecks tha t arise at extreme scales. In this work\, we introduce the asynchronous DG (ADG) method\, which combines the benefits of the DG method with asynchro nous computing by relaxing the need for data communication and synchroniza tion at the mathematical level. The proposed ADG method ensures local cons ervation and effectively addresses challenges arising from asynchrony. To assess its stability\, we employ Fourier-mode analysis to examine the diss ipation and dispersion behavior of fully-discrete DG and ADG schemes with the Runge-Kutta (RK) time integration schemes across a wide range of waven umbers. Furthermore\, we present an error analysis demonstrating that the ADG method with standard numerical fluxes achieves at most first-order acc uracy. To recover accuracy\, we derived asynchrony-tolerant (AT) fluxes th at utilize data from multiple time levels. Finally\, extensive numerical e xperiments are conducted to validate the performance and accuracy of the A DG-AT scheme for both linear and nonlinear problems.\n\nWith the developme nt of the asynchronous discontinuous Galerkin (ADG) method\, we finally pu t our focus on implementing and evaluating its performance in solving hype rbolic equations with shocks/discontinuities.\n\nTo achieve this\, we chos e a highly scalable DG solver for compressible Euler equations from deal.I I\, which is one of the widely used open-source finite element libraries. The solver uses low-storage explicit Runge-Kutta schemes for the time inte gration. We implemented the ADG method in deal.II\, incorporating the comm unication-avoiding algorithm (CAA)\, and performed accuracy validation and scalability benchmarks. The results showcase the accuracy limitations of standard ADG schemes and the effectiveness of newly developed asynchrony-t olerant (AT) fluxes. Strong scaling results are provided for both synchron ous and asynchronous DG solvers\, demonstrating a speedup of up to 80% wit h the ADG method at an extreme scale with 9216 cores.\n\nThis thesis focus ed on the development of scalable PDE solvers based on the asynchronous di scontinuous Galerkin method for massively parallel flow simulations. Altho ugh these advancements were specifically geared towards the DG method\, th ey are also applicable to the finite volume (FV) method and can be easily integrated into commercial FV-based PDE solvers. The overall work highligh ts the potential benefits of the asynchronous approach for the development of accurate and scalable DG and FV-based PDE solvers\, paving the way for simulations of complex physical systems on massively parallel supercomput ers.\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:20230806T150000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR