Robust and efficient validation of the linear hexahedral element
For finite element analysis practitioners, this provides a fast and reliable mesh validity check for hexahedral elements, which was previously non-trivial.
The paper presents a method for robustly and efficiently checking the validity of linear hexahedral elements in finite element analysis, achieving a speed of about 6 million hexahedra per second on a single core.
Checking mesh validity is a mandatory step before doing any finite element analysis. If checking the validity of tetrahedra is trivial, checking the validity of hexahedral elements is far from being obvious. In this paper, a method that robustly and efficiently compute the validity of standard linear hexahedral elements is presented. This method is a significant improvement of a previous work on the validity of curvilinear elements. The new implementation is simple and computationally efficient. The key of the algorithm is still to compute Bézier coefficients of the Jacobian determinant. We show that only 20 Jacobian determinants are necessary to compute the 27 Bézier 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, \ie write a simple code that takes the coordinates of 8 points as input and outputs the validity of the hexahedron.