Fast practical untangling of simplicial P2 and P3 curvilinear meshes

The aim of this article is to couple the ideas proposed by [1,2] and [3] 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 [3] 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.