Fast Gradient‐Limited Sizing Function for High‐Quality Surface Mesh Generation

ABSTRACT The sizing function is essential for generating high‐quality meshes efficiently. To address the issues of abrupt size transitions and the high computational costs present in existing sizing function algorithms, we propose the first LP‐based global gradient‐limited sizing function with adaptive error control for unstructured mesh generation. Building upon an established convex optimization model, the method employs a piecewise linear approximation of the nonlinear gradient constraints, reducing model complexity. A rigorous error analysis quantifies the approximation accuracy and guides the design of an adaptive refinement strategy that balances constraint accuracy with computational efficiency. Numerical experiments demonstrate that the proposed algorithm consistently achieves smooth and well‐controlled size transitions, exhibits superior time efficiency, and generates high‐quality meshes, outperforming nonlinear programming, GradH‐correction, and H‐correction approaches. These results confirm the effectiveness and robustness of the LP‐based framework and highlight its suitability for large‐scale engineering applications.