Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community.
On October 1, 2024, Daniele Panozzo from Courant Institute and NYU presented "Geometric Predicates for Unconditionally Robust Elastodynamics Simulation." The numerical solution of partial differential equations (PDE) is ubiquitously used for physical simulation in scientific computing and engineering. Ideally, a PDE solver should be opaque: the user provides as input the domain boundary, boundary conditions, and the governing equations, and the code returns an evaluator that can compute the value of the solution at any point of the input domain. This is surprisingly far from being the case for all existing open-source or commercial software, despite the research efforts in this direction and the large academic and industrial interest. To a large extent, this is due to lack of robustness in geometric algorithms used to create the discretization, detect collisions, and evaluate element validity. I will present the incremental potential contact simulation paradigm, which provides strong robustness guarantees in simulation codes, ensuring, for the first time, validity of the trajectories accounting for floating point rounding errors over an entire elastodynamic simulation with contact. A core part of this approach is the use of a conservative line-search to check for collisions between geometric primitives and for ensuring validity of the deforming elements over linear trajectories. I will discuss both problems in depth, showing that SOTA approaches favor numerical efficiency but are unfortunately not robust to floating point rounding, leading to major failures in simulation. I will then present an alternative approach based on judiciously using rational and interval types to ensure provable correctness, while keeping a running time comparable with non-conservative methods. To conclude, I will discuss a set of applications enabled by this approach in microscopy and biomechanics, including traction force estimation on a live zebrafish and efficient modeling and simulation of fibrous materials.
Learn more about MFEM at mfem.org/ and view the seminar speaker lineup at mfem.org/seminar/. LLNL-VIDEO-2001923
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