New quality measures for quadrilaterals and new discrete functionals for grid generation
Abstract
In this paper, we review some grid quality metrics Robinson1987, Lo1989, Field2000, Knupp2001, Remacle2012 and define some new quality measures for quadrilateral elements. Usually, a maximum value of a quality measure corresponds to the minimum value of the energy density over the grid Ivanenko2000. We also define new discrete functionals which are implemented as objective functions in an optimizationbased method for quadrilateral grid generation and improvement. These functionals are linearly combined with a discrete functional whose domain has an infinite barrier at the boundary of the set of unfolded grids like $S_{\omega,\epsilon}(G)$, see Barrera2010, in order to preserve convex grid cells in each step of the optimization process.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.10634
 Bibcode:
 2022arXiv220510634G
 Keywords:

 Mathematics  Numerical Analysis
 EPrint:
 13 pages, 8 figures