Work

An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.18308

Authors: Zhen, Yicun, Zhu, Shouxian, Mao, Shipeng

Institutions: Hohai University, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G7179921162

OpenAlex ID: W7213528729

Cites: 20

Cited by:

Related to: 10