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Robust and efficient validation of the linear hexahedral element

Johnen, Amaury, Jean-Christophe Weill, Jean-François Remacle

Proceedings, 26th International Meshing Roundtable, Elsevier, Science Direct, September 18-21 2017

INTERNATIONAL
MESHING
ROUNTABLE

26th International Meshing Roundtable
Barcelona, Spain
September 18-21, 2017

Amaury Johnen, Université catholique de Louvain, BE, amaury.johnen@uclouvain.be
Jean-Christophe Weill, CEA, FR, Jean-Christophe.WEILL@CEA.FR
Jean-François Remacle, Université catholique de Louvain, BE, jean-francois.remacle@uclouvain.be

Abstract
Checking mesh validity is a mandatory step before doing any finite element analysis. If checking the validity of tetrahedra is trivial, verifying hexahedral elements is far from being obvious. The generation of hex-dominant meshes in an indirect fashion tends to produce a large amount of hexahedra that could potentially be invalid. In this paper, a method that robustly and efficiently compute the validity of the standard linear hexahedral element is presented. This method is an improvement of a previous work on the validity of curvilinear elements. The new implementation is optimal, simple to code and is computationally efficient. The basis of the algorithm is still to compute B\'ezier coefficients of the Jacobian determinant. Here, we show that only $20$ Jacobian determinants are necessary to compute the $27$ B\'ezier coefficients. Those $20$ Jacobians can be efficiently computed by calculating the volume of $20$ tetrahedra. The new implementation is able to check the validity of about $6$ million hexahedra per second on one core of a personal computer. Through the paper, all the necessary information is provided that allow to easily reproduce the results i.e. write a simple code that takes the coordinates of $8$ points as input and outputs the validity of the hexahedron.

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