Curve resampling based high-quality high-order unstructured quadrilateral mesh generation

2026-03-24

AI Summary

Existing methods struggle to simultaneously preserve boundary fidelity, ensure element quality, and maintain computational efficiency when generating high-order quadrilateral meshes in complex geometries, often resulting in degenerate or inverted elements. This work proposes an indirect generation framework that reformulates high-order mesh optimization as a curve reconstruction problem with bounded geometric error. By integrating optimization-driven curve resampling and implicit interface consistency constraints, the approach significantly reduces computational complexity while guaranteeing geometric fidelity and element validity. The method efficiently produces inversion-free, high-quality unstructured high-order quadrilateral meshes, demonstrating excellent numerical stability and adaptability across complex geometries.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve efficient generation, particularly for complex geometries where degenerate and inverted elements frequently occur. To address this issue, this paper proposes a high-quality high-order unstructured quadrilateral mesh generation method based on geometric error-bounded curve reconstruction, which employs an indirect approach to enforce interface consistency. By optimization-based curve reconstruction strategies, our method improves mesh quality while maintaining the validity of high-order elements. Compared to direct high-order mesh optimization techniques, our approach reduces the optimization problem to curve reconstruction problem, significantly lowering computational complexity and enhancing efficiency. Experimental results demonstrate that the proposed method efficiently generates high-quality high-order quadrilateral meshes while preserving boundary/interface geometric features, offering improved adaptability and numerical stability in complex geometries.

Problem

• high-order quadrilateral mesh
• boundary preservation
• mesh quality
• complex geometries
• degenerate elements

Innovation

• high-order quadrilateral mesh
• curve resampling
• geometric error-bounded reconstruction
• interface consistency
• mesh quality optimization