MINIMIZATION OF THE DISTORTION OF QUADRILATERAL AND HEXAHEDRAL MESHES

In this paper a minimization algorithm of the mesh distortion metric proposed by Oddy is presented. It is valid for meshes composed by quadrilateral or hexahedral elements. Although it has been extensively used, the original definition has several limitations that preclude its use in a minimization procedure. For instance, it is only valid for convex quadrilaterals or hexahedra, and it gives an infinite distortion value for a degenerated quadrilateral with triangular shape. In order to overcome these drawbacks, in this work we deduce a geometrical interpretation of the original distortion metric. Based on this interpretation, we first develop a new alternative to compute the distortion metric; and second, we extend the original distortion metric to non-convex quadrilaterals and hexahedra. Then; a minimization algorithm of the improved distortion metric based on a Newton-Raphson method is developed. It is important to note that the original and the improved definition of the distortion metric coincide around the optimal solution. Finally, some numerical examples are presented to assess the robustness of this algorithm.