Generation of High-Order Coarse Quad Meshes on CAD Models via Integer Linear Programming

TL;DR

This paper introduces an end-to-end method for generating high-quality, high-order coarse quadrilateral meshes on CAD models using integer linear programming, enabling advanced analysis techniques with improved mesh quality.

Contribution

The paper presents a novel pipeline that formulates quad mesh simplification as an integer linear programming problem, ensuring robustness and feature preservation.

Findings

The approach is fast and robust.

It strictly respects CAD features.

It produces coarse, high-quality quad meshes.

Abstract

We propose an end-to-end pipeline to robustly generate high-quality, high-order and coarse quadrilateral meshes on CAD models. This kind of mesh enables the use of high-order analysis techniques such as high-order finite element methods or isogeometric analysis. An initial unstructured mesh is generated; this mesh contains a low number of irregular vertices but these are not necessarily aligned, causing a very dense quad layout. A T-mesh is built on the mesh which allows to modify its topology by assigning new integer lengths to the T-mesh arcs. The task of simplifying the quad layout can be formulated as an Integer Linear Program which is solved efficiently using an adequate solver. Finally, a high-order quad mesh is extracted from the optimized topology. Validation on several CAD models shows that our approach is fast, robust, strictly respects the CAD features, and achieves interesting results in terms of coarseness and quality.