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Explore a novel field remap method for multimaterial Arbitrary Lagrangian–Eulerian (ALE) hydrodynamics in this 27-minute conference talk from the MFEM Workshop 2025. Learn how LLNL's Vladimir Tomov addresses the challenge of remapping fields between initial and final meshes through a two-step approach combining direct interpolation in physical space with optimization strategies. Discover how GPU-accelerated interpolation routines from the GSLIB library enable computationally practical direct interpolation that produces bounded fields with low diffusion, though without conservation guarantees. Understand two complementary optimization strategies used to recover conservation while maintaining physical bounds: interior-point methods implemented in HiOp optimization library and the Proximal Galerkin framework that performs optimization in a latent space with inherent bound enforcement. Examine how this approach achieves minimal diffusion for finite element fields of arbitrary order, supports direct remapping of integration-point quantities without projection onto finite element spaces, and circumvents synchronization difficulties between primal variables and conserved quantities found in advection-based remap methods. Review demonstration results on standard 2D and 3D benchmarks as well as full ALE hydrodynamics simulations, presented as part of the fifth annual MFEM community workshop that brings together users and developers of the Modular Finite Element Methods project for high-order mathematical calculations in large-scale scientific simulations.
