Remap for ALE Hydrodynamics via Direct Interpolation and Constraint Optimization
Abstract
This work presents an optimization-based remap approach for arbitrary Lagrangian-Eulerian (ALE) hydrodynamics that preserves sharp features and physical bounds while conserving global quantities such as volume, mass, momentum, and total energy. Achieving these properties is the main challenge in remap methods. The presented approach is well-suited for high-order finite element (FE) discretizations and ALE methods that allow for large, purely Lagrangian displacements between successive remeshing and remapping steps. Recent advances in parallel, GPU-capable interpolation routines enable the initial transfer of all fields via direct physical-space interpolation, avoiding computationally costly and diffusive pseudo-transient PDE-based advection. The interpolation produces bounded fields with minimal numerical diffusion. However, it may violate the desired conservation of global properties. Thus, a subsequent optimization step restores conservation while preserving physical bounds. The presented method provides minimally diffusive remapping of finite element fields of arbitrary order. Moreover, it directly remaps quantities defined at integration points, eliminating the need for projection onto finite element spaces. The approach also mitigates typical challenges associated with synchronizing primal variables and conserved quantities in advection-based remap methods. The proposed optimization-based remap method is evaluated using standard two- and three-dimensional remap benchmarks and full ALE hydrodynamics simulations.
Related
- Constraint Preserving AFD-WENO Schemes for Relativistic Hydrodynamics with General Equations of State
- Entropy-Stable and Physical-Constraint-Preserving DGSEM for Symmetry-Reduced General-Relativistic Hydrodynamics on Stationary Spacetimes
- A Direct Approach to Hermite Interpolation
- Minimum-Norm Interpolation in Weighted Variation Spaces: Direct and Inverse Problems
- Birkhoff interpolation models for optimization with some available derivatives
BibTeX
@misc{keith2026remap,
title = {{Remap for ALE Hydrodynamics via Direct Interpolation and Constraint Optimization}},
author = {Brendan Keith and Dohyun Kim and Boyan Lazarov and Ketan Mittal and Cosmin G. Petra and Mathias R. Schmidt and Vladimir Z. Tomov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05327},
eprint = {2611.05327},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05327},
}
RIS
TY - UNPB
TI - Remap for ALE Hydrodynamics via Direct Interpolation and Constraint Optimization
AU - Brendan Keith
AU - Dohyun Kim
AU - Boyan Lazarov
AU - Ketan Mittal
AU - Cosmin G. Petra
AU - Mathias R. Schmidt
AU - Vladimir Z. Tomov
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05327
UR - https://arxiv.org/abs/2611.05327
AB - This work presents an optimization-based remap approach for arbitrary Lagrangian-Eulerian (ALE) hydrodynamics that preserves sharp features and physical bounds while conserving global quantities such as volume, mass, momentum, and total energy. Achieving these properties is the main challenge in remap methods. The presented approach is well-suited for high-order finite element (FE) discretizations and ALE methods that allow for large, purely Lagrangian displacements between successive remeshing and remapping steps. Recent advances in parallel, GPU-capable interpolation routines enable the initial transfer of all fields via direct physical-space interpolation, avoiding computationally costly and diffusive pseudo-transient PDE-based advection. The interpolation produces bounded fields with minimal numerical diffusion. However, it may violate the desired conservation of global properties. Thus, a subsequent optimization step restores conservation while preserving physical bounds. The presented method provides minimally diffusive remapping of finite element fields of arbitrary order. Moreover, it directly remaps quantities defined at integration points, eliminating the need for projection onto finite element spaces. The approach also mitigates typical challenges associated with synchronizing primal variables and conserved quantities in advection-based remap methods. The proposed optimization-based remap method is evaluated using standard two- and three-dimensional remap benchmarks and full ALE hydrodynamics simulations.
ER -