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Indirect all-quadrilateral meshing based on bipartite topological labeling

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Abstract

Quadrilateral meshes offer certain advantages compared to triangular ones, such as reduced number of elements and alignment with problem-specific directions. We present a pipeline for the generation of quadrilateral meshes on complex geometries. It is based on two key components: robust surface meshing and efficient indirect conversion of a triangular mesh to an all-quad one. The input is a valid geometric surface mesh, i.e., a triangulation that accurately represents the geometry of the model. A right-angled triangular surface mesh is initially created by continuously modifying the input mesh while always preserving its topological validity. The main advantages of our local mesh modification-based approach are to (i) allow the generation of meshes that are globally aligned with a given direction field and (ii) to reliably handle non-manifold feature edges (in multi-volume models) and small features. The final quadrilateral mesh is obtained by merging pairs of triangles into quadrilaterals. We develop a novel bipartite labeling scheme in order to identify and correct inconsistent pairings. The procedure is based on local operations and is much more efficient than previous global strategies for tri-to-quad conversion. The whole pipeline is tested on a large number of models with diverse characteristics.

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  1. Maxence Reberol and Jean-François Remacle are contributing authors.

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  1. Institute of Mechanics, Materials and Civil Engineering, Université Catholique de Louvain, Avenue Georges Lemaitre 4, 1348, Louvain-la-Neuve, Belgium

    Christos Georgiadis, Maxence Reberol & Jean-François Remacle

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  1. Christos Georgiadis
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Correspondence to Christos Georgiadis.

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This study was carried out in the framework of the research project ‘Hextreme,’ funded by the European Research Council (ERC-2015-AdG-694020) and hosted at the Université catholique de Louvain. The authors have no competing interests to declare that are relevant to the content of this article.

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Georgiadis, C., Reberol, M. & Remacle, JF. Indirect all-quadrilateral meshing based on bipartite topological labeling. Engineering with Computers 38, 4731–4747 (2022). https://doi.org/10.1007/s00366-022-01740-4

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