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 $S_{\omega,\epsilon}(G)$, see Barrera2010, in order to preserve convex grid cells in each step of the optimization process.
翻译：在本文中,我们审查了一些网格质量指标Robinson1987、Lo1989、Field2000、Knupp2001、Remacle 1212,并界定了四边元素的一些新的质量措施。通常,质量措施的最大值相当于Ivanenko2000网格中能量密度的最小值。我们还界定了新的离散功能,这些功能是在基于优化的四边网的生成和改进方法中作为客观功能实施的。这些功能与一个离散功能是线性结合的,该功能的域在一套开阔的网格的边界上有着无限的屏障,例如,S ⁇ omega,\epsilon}(G)$,见Barrera2010,以便在优化进程的每个步骤中保存锥形网格。
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