Surface reparametrization using quadratic finite elements
Beaufort, Pierre-Alexandre, Jean-François Remacle
Research Note, 25th International Meshing Roundtable, Sandia National Laboratories, September 26-30 2016
25th International Meshing Roundtable
Washington DC, U.S.A.
September 26-30, 2016
Pierre-Alexandre Beaufort, Université catholique de Louvain, Institute of Mechanics, Materials and Civil engineering (iMMC), BE, firstname.lastname@example.org
Jean-François Remacle, Université catholique de Louvain, Institute of Mechanics, Materials and Civil engineering (iMMC), BE, email@example.com
Research Note Abstract
The present paper tackles the challenges for one-to-one quadratic finite element mappings for high order reparametrization purposes.
To our best knowledge, it is a first of its kind and this paper enlights specific problems related to the computation of high order discrete harmonic maps. First, the harmonic mapping from poor quality triangulations is not guaranteed to be bijective and standard convexity arguments do not apply anymore in the high order case.
Then, quadratic mappings generate curved parametric triangles that should be valid in order to ensure the correctness of the transformation.
Here, we propose a two step procedure that ensures bijectivity: i) curvilinear parametric triangles are generated through a standard finite element procedure and ii) invalid parametric triangles are
Examples of parameterizations generated with Gmsh are shown.
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