PreprintCC BY 4.0arXiv
An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods
Abstract
It is mathematically proved that, for a grid under a boundary-preserving piecewise-smooth deformation, the positivity of the Jacobian determinant in each closed element is also a sufficient condition for the deformed grid to remain valid. Most of the proof is devoted to showing that the element-wise positivity of the Jacobian indeed induces a local isomorphism in the grid-deformation setting. This result provides users of ALE methods and of the generalized Lagrangian method with a clean answer: checking the Jacobian alone is enough to determine the validity of the deformed grid.
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BibTeX
@misc{zhen2026efficient,
title = {{An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods}},
author = {Yicun Zhen and Shouxian Zhu and Shipeng Mao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18308},
eprint = {2609.18308},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18308},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods
AU - Yicun Zhen
AU - Shouxian Zhu
AU - Shipeng Mao
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.18308
UR - https://arxiv.org/abs/2609.18308
AB - It is mathematically proved that, for a grid under a boundary-preserving piecewise-smooth deformation, the positivity of the Jacobian determinant in each closed element is also a sufficient condition for the deformed grid to remain valid. Most of the proof is devoted to showing that the element-wise positivity of the Jacobian indeed induces a local isomorphism in the grid-deformation setting. This result provides users of ALE methods and of the generalized Lagrangian method with a clean answer: checking the Jacobian alone is enough to determine the validity of the deformed grid.
ER -