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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

INTERNATIONAL
MESHING
ROUNTABLE

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, pierre-alexandre.beaufort@uclouvain.be
Jean-François Remacle, Université catholique de Louvain, Institute of Mechanics, Materials and Civil engineering (iMMC), BE, jean-francois.remacle@uclouvain.be

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 subsequently untangled. Examples of parameterizations generated with Gmsh are shown.

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