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:35@cds.iisc.ac.in DTSTART;TZID=Asia/Kolkata:20240207T100000 DTEND;TZID=Asia/Kolkata:20240207T110000 DTSTAMP:20240207T172508Z URL:https://cds.iisc.ac.in/events/ph-d-thesis-colloquium-cds-a-scalable-as ynchronous-discontinuous-galerkin-method-for-massively-parallel-pde-solver s/ SUMMARY:Ph.D. Thesis {Colloquium}: CDS : "A scalable asynchronous discontin uous-Galerkin method for massively parallel PDE solvers." DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Col loquium\n\n\n\n\n\n\n\n\n\n\n\nSpeaker  : Mr. Shubham Kumar Goswami\n\nS. R. Number  : 06-18-00-10-12-19 -1-17224\n\nTitle :  "A scalable asynchro nous discontinuous-Galerkin method for massively parallel PDE solvers "\n\ nResearch Supervisor:  Dr. Konduri Aditya\nDate &\; Time  : February 07\, 2024 (Wednesday) at 10:00 AM\nVenue   : The Thesis Colloquium will b e held on HYBRID Mode\n# 102 CDS Seminar Hall /MICROSOFT TEAMS.\n\n\n\n\nP lease click on the following link to join the Thesis Colloquium:\n\nMS T eams link\n\n\n\n\n\n\nABSTRACT\n\n\n\n\n\n\n\n\n\nAccurate simulations of turbulent flows in computational fluid dynamics (CFD) are crucial for com prehending numerous complex phenomena in engineered systems and natural pr ocesses. These flows are governed by nonlinear partial differential equati ons (PDEs)\, which are approximated as algebraic equations and solved usin g PDE solvers. However\, the complexity of turbulence makes these simulati ons computationally expensive\, necessitating the use of massively paralle l supercomputers. While advancements such as hardware-aware computing\, fa ult tolerance\, and overlapping computation and communication have improve d solver scalability\, achieving efficient performance at extreme scales r emains a challenge owing to the communication and synchronization overhead . To address this issue\, an asynchronous computing approach was introduce d that relaxed communication and synchronization at a mathematical level\, allowing PEs to operate independently regardless of the status of message s\, potentially decreasing communication overhead and enhancing scalabilit y. This approach has been developed specifically for finite difference sch emes\, which are widely used but not ideal for complex geometries and unst ructured meshes. The objective of this work is to develop an asynchronous discontinuous-Galerkin method that can provide high-order accurate solutio ns for various flow problems on unstructured meshes and demonstrate its sc alability.\n\n\n\n\nBased on the asynchronous computing approach\, several PDE solvers have been developed that use high-order asynchrony-tolerant f inite difference schemes for spatial discretization to simulate reacting a nd non-reacting turbulent flows\, achieving significant improvements in sc alability. However\, for time integration\, most of them used either multi -step Adams-Bashforth schemes\, which possess poor stability\, or multi-st age Runge-Kutta (RK) schemes with an over-decomposed domain that necessita tes larger message sizes for communication and redundant computations. In this work\, we propose a novel method to couple asynchrony-tolerant and lo w-storage explicit RK (LSERK) schemes to solve time-dependent PDEs with re duced communication efforts. We developed new asynchrony-tolerant schemes for ghost or buffer point updates that are necessary to maintain the desir ed order of accuracy. The accuracy of this method has been investigated bo th theoretically and numerically using simple one-dimensional linear model equations. Thereafter\, we demonstrate the scalability of the proposed nu merical method through three-dimensional simulations of decaying Burgers ’ turbulence performed using two different asynchronous algorithms: comm unication-avoiding and synchronization-avoiding algorithms. Scalability st udies up to 27\,000 cores yielded a speed-up of up to 6× compared to a ba seline synchronous algorithm.\n\n\n\n\nIn recent years\, the discontinuous Galerkin (DG) method has received broad interest in developing PDE solver s\, particularly for nonlinear hyperbolic problems\, due to its ability to provide high-order accurate solutions in complex geometries\, capture dis continuities\, and exhibit high arithmetic intensity. However\, the scalab ility of DG-based solvers is hindered by communication bottlenecks that ar ise at extreme scales. In this work\, we introduce the asynchronous DG (AD G) method\, which combines the benefits of the DG method with asynchronous computing by relaxing the need for data communication and synchronization at the mathematical level to overcome communication bottlenecks. The prop osed ADG method ensures flux conservation and effectively addresses challe nges arising from asynchrony. To assess its stability\, we employ Fourier- mode analysis to examine the dissipation and dispersion behavior of fully- discrete DG and ADG schemes with the Runge-Kutta (RK) time integration sch emes across the entire range of wavenumbers. Furthermore\, we present an e rror analysis within a statistical framework\, which demonstrates that the ADG method with standard numerical fluxes achieves at most first-order ac curacy. To recover accuracy\, we derived asynchrony-tolerant (AT) fluxes t hat utilize data from multiple time levels. Finally\, extensive numerical experiments are conducted to validate the performance and accuracy of the ADG-AT scheme for both linear and nonlinear problems.\n\n\n\n\nWith the de velopment of the asynchronous discontinuous-Galerkin (ADG) method\, we fin ally put our focus on implementing and evaluating its performance in solvi ng hyperbolic equations with shocks/discontinuities. To achieve this\, we chose a highly scalable DG solver for compressible Euler equations from de al.II\, which is one of the widely used open-source finite element librari es. The solver uses low-storage explicit Runge-Kutta schemes for the time integration. We implemented the ADG method in deal.II\, incorporating the communication-avoiding algorithm (CAA)\, and performed validation and benc hmarking\, showcasing the accuracy limitations of standard ADG schemes and the effectiveness of newly developed asynchrony-tolerant (AT) fluxes. Str ong scaling results are provided for both synchronous and asynchronous DG solvers\, demonstrating a speedup of up to 80%. Since these AT fluxes are also compatible with the finite volume (FV) method\, the overall work high lights the potential benefits of the asynchronous approach for the develop ment of accurate and scalable DG and FV-based PDE solvers\, paving the way for simulations of complex physical systems on massively parallel superco mputers.\n\n\n\n\n\n\n\nALL ARE WELCOME\n\n CATEGORIES:Events,Thesis Defense END:VEVENT BEGIN:VTIMEZONE TZID:Asia/Kolkata X-LIC-LOCATION:Asia/Kolkata BEGIN:STANDARD DTSTART:20230207T100000 TZOFFSETFROM:+0530 TZOFFSETTO:+0530 TZNAME:IST END:STANDARD END:VTIMEZONE END:VCALENDAR