Aspect‐Ratio Preserving Target‐Matrix Optimization With Linesweep Smoothing for Arbitrary Lagrangian–Eulerian Meshes With Adaptive Refinement

Abstract

ABSTRACT We present a rezoning method for three‐dimensional arbitrary Lagrangian–Eulerian (ALE) and ALE with adaptive mesh refinement (ALE‐AMR) simulations. The method combines linesweep smoothing with an aspect‐ratio‐preserving target‐matrix optimization paradigm (TMOP) formulation. It is designed to preserve anisotropic mesh structures produced by the Lagrangian phase while maintaining mesh validity and reducing shear, sliver formation, and cell bunching in block‐structured, optionally nonconformal meshes. The approach combines a patch‐local TMOP objective and a convexity‐based disentanglement metric within an existing linesweep framework. The TMOP target matrix is built from local edge geometry and includes a prescribed aspect‐ratio cap, which provides an explicit control parameter for mesh relaxation. The metric is evaluated on an extended nodal patch, so that the objective couples the motion of a node to the quality of neighboring elements affected by that motion. Combined with sequential updates, this ensures that accepted steps are tested against the updated quality of the local coupled patch, rather than only against the elements directly incident on the node. When invalid configurations are detected, the TMOP objective is replaced by a convexity objective that drives signed volumes back to positive values. Parallelism is recovered through a distance‐1 coloring of the nodal graph, allowing independent node updates to be performed concurrently. Mesh‐only and hydrodynamic tests assess shear reduction, aspect‐ratio control, and mesh validity. Among the configurations examined, only the TMOP combined method consistently satisfies these requirements together while retaining anisotropic mesh structures, with no observed invalid post‐rezoning states. The prescribed target cap provides explicit control over excessive elongation without imposing an isotropic target. Strong and weak scaling measurements quantify the cost of the parallel optimization.

The authors' abstract, as published at the source. International Journal for Numerical Methods in Engineering, 2026 · DOI ↗