New quality measures for quadrilaterals and new discrete functionals for grid generation

2022/05/21 by Guilmer González Flores, Flores, Guilmer González, Pablo Barrera Sánchez +1
Computer Science · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2205.10634

13 pages, 8 figures

arxiv created 2022/05/21 · arxiv updated 2022/05/24

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 optimization-based 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_ω,ε(G), see Barrera2010, in order to preserve convex grid cells in each step of the optimization process.

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