Fast practical untangling of simplicial P2 and P3 curvilinear meshes

Coiffier, Guillaume;Johnen, Amaury;Remacle, Jean-François
(2025) 2025 SIAM International Meshing Roundtable (IMR) — Location: Fort Worth, TX (3.March.2025)

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The aim of this article is to couple the ideas proposed by [8, 6] and [4] to unfold/untangle high-order meshes. What is proposed here is to systematically reduce the untangling of any high-order elements to the problem of untangling simplices (triangles in 2D and tetrahedra in 3D). First, we present a general way of expressing the validity of a high-order element by calculating linear combinations of areas of well-chosen simplices. We then show how to adapt[4] to these linear combinations of simplices. Examples of 2D boundary layer untangling are presented with P2 and P3 elements. The algorithm is then adapted to P2 tetrahedra.
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Coiffier, G., Johnen, A., & Remacle, J.-F. (2025). Fast practical untangling of simplicial P2 and P3 curvilinear meshes. Proceedings of the 2025 SIAM International Meshing Roundtable, p. 113-125. https://doi.org/10.1137/1.9781611978575.10