CIGMO seminars will be held in a hybrid format, with options for both in-person attendance at the host university and virtual participation via Zoom.
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| Dec 10, 2025 | MFEM: Accelerating Efficient Solution of PDEs at Exascale - Speaker: Tzanio Kolev (Lawrence Livermore National Laboratory)
- Date: December 10, 2025
- Time: 11:00 – 12:00 (EST)
- Abstract: High-order finite element methods provide a powerful framework for solving partial differential equations on unstructured grids. These methods are particularly well-suited for exascale architectures with GPU accelerators, where their efficiency and scalability rely on the adoption of partially assembled algorithms that reduce memory data motion. The matrix-free nature of partial assembly algorithms enables higher efficiency, but also motivates new research in areas such as preconditioning and monotonicity. In this talk we review recent work on GPU-oriented algorithms and software for high-order meshing, discretizations and solvers, and demonstrate their impact in several large-scale applications from the US Department of Energy. Many of these developments have been incorporated in MFEM (https://mfem.org), a scalable library for high-order finite element discretization of PDEs on general unstructured grids that employs partial assembly and matrix-free algorithms to power a wide variety of HPC applications. In addition to discussing MFEM’s capabilities and algorithms, we also report on some of the work in related projects, including high-order ALE compressible hydrodynamics in LLNL’s BLAST code; GPU benchmarks from the Center for Efficient Exascale Discretizations in the US Exascale Computing Project; and the Cascadia project for acoustic–gravity waves in tsunami modeling.
- Location: Virtual (Zoom)
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- Recordings: Zoom Recording
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| Nov 07, 2025 | Efficient optimization-based invariant-domain-preserving limiters for gas dynamics equations - Speaker: Xiangxiong Zhang (Purdue University)
- Date: November 7, 2025
- Time: 11:00 – 12:00 (EST)
- Abstract: I will present effective splitting methods for implementing optimization-based limiters to enforce the invariant domain defined by positive density and positive internal energy. Both L2 and L1 norm minimization limiters will be considered. The key ingredients include an efficient explicit formulation of the projection onto the invariant domain set, and also proper applications of the classical Douglas-Rachford splitting and its more recent extension Davis-Yin splitting. Such an optimization-based approach can be applied to many numerical schemes to construct high order accurate, globally conservative, and invariant-domain-preserving schemes for compressible flow equations. As a demonstration, we apply it to high order discontinuous Galerkin schemes with non-SSP Runge-Kutta and test it on demanding benchmarks to validate the robustness and performance. Unlike L1 minimization in many other applications, the L1 minimization does not produce a significantly more sparse solution than L2 minimization in this context of limiters. On the other hand, for special problems such as high speed astrophysical jets, L1-norm limiter is triggered less during the time evolution than L2-norm limiter, thus L1-norm limiter seems better for these problems.
- Location: Virtual (Zoom)
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| Oct 29, 2025 | Shocks without tracking or capturing: Exceeding 1 quadrillion degrees of freedom via inviscid regularization of the compressible Navier-Stokes - Speaker: Spencer Bryngelson (Georgia Institute of Technology)
- Date: October 29, 2025
- Time: 11:00 – 12:00 (EST)
- Abstract: A method for solving multi-species and shock-laden flow at unprecedented problem sizes and time-to-solution is presented. The first inviscid regularization of the Navier-Stokes-like PDE is performed. This enables linear and well-conditioned numerics suitable for mixed-precision computation. A unified memory implementation is crafted for tightly coupled CPU-GPU and APU architectures (e.g., MI250X, GH200, MI300A), now standard on flagship machines like El Capitan and Frontier. With this trio, we improve on state-of-the-art CFD techniques with order of magnitude improvements along computational cost and memory footprint axes. The reduced memory footprint compared to baselines enables, for example, 25-times larger simulations, here shown to exceed 1 quadrillion degrees of freedom (200T grid points) with per-grid-point cost speedups. The method strong scales from 8 nodes to the full systems (>10K nodes) with better than 50% efficiency. This enables, for example, a typical 200B grid point CFD simulation in less than one wall clock minute on OLCF Frontier. Early results suggest increased robustness compared to ENO/limiter-type shock capturing schemes for high-Mach flows and strong discontinuities. Results are shown for a Mach 14 many-rocket-engine configuration that nominally matches the SpaceX Super Heavy.
- Location: Virtual (Zoom)
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- Recordings: Zoom Recording
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| Sep 24, 2025 | A priori error analysis of the proximal Galerkin method - Speaker: Rami Masri (Brown University)
- Date: September 24, 2025
- Time: 11:00 – 12:00 (EST)
- Abstract: The proximal Galerkin (PG) method is a finite element method for solving variational problems with inequality constraints. It has several advantages, including constraint-preserving approximations and mesh independence. This talk presents the first abstract a priori error analysis of the PG method, providing a general framework to establish convergence and error estimates. As applications of the framework, we demonstrate optimal convergence rates for both the obstacle and Signorini problems using various finite element subspaces.
- Location: 170 Hope St., Room 108, Providence, RI.
- Zoom: Zoom Link
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