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

@article{Flores2022NewQM,
  title={New quality measures for quadrilaterals and new discrete functionals for grid generation},
  author={Guilmer F. Gonz{\'a}lez Flores and Pablo Barrera Sanchez},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.10634}
}
Summary In this paper, we review some grid quality metrics 1,2,3,4,5 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 6 . 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… 

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References

SHOWING 1-10 OF 26 REFERENCES
Barrier variational generation of quasi‐isometric grids
TLDR
A fast and reliable grid untangling procedure based on the penalty-like reformulation of barrier functional and the continuation technique is described and demonstrates that the suggested functional produces high-quality grids with small global condition numbers.
A two-dimensional paving mesh generator for triangles with controllable aspect ratio and quadrilaterals with high quality
TLDR
The mesh generator presented here can render triangles with high aspect ratios through a paving algorithm, and quadrilateral meshes converted from the mesh generator introduced here have a considerably better quality than those converted from several other triangular mesh generators.
Shape Measures for Quadrilaterals, Pyramids, Wedges, and Hexahedra
  • B. Joe
  • Geology, Mathematics
  • 2008
Shape measures for triangles and tetrahedra are used to derive shape measures for plane and space quadrilaterals, pyramids, wedges, and hexahedra. Valid space quadrilaterals, pyramids, wedges, and
Generating quadrilateral elements on plane and over curved surfaces
Laplacian-Isoparametric Grid Generation Scheme
An alternative to the commonly employed Laplacian grid generation scheme for finite element problems is developed. The procedure is based upon a local quadratic isoparametric transformation. The
A robust elliptic grid generator
Control of cell shapes in the course of grid generation
TLDR
The proposed approach is based on the principle of minimum mapping-energy density, which can be applied to both structured and unstructured meshing, and ensures that the resulting grid is orthogonal at the domain boundary or at the boundary between two blocks with the mesh condensed toward the boundary.
A New Smoothing Algorithm for Quadrilateral and Hexahedral Meshes
  • S. Khattri
  • Computer Science
    International Conference on Computational Science
  • 2006
TLDR
A new smoothing called parallelogram smoothing is derived that tries to fit a given domain by the parallelograms and is superior to the traditional Laplacian smoothing.
Smoothness and Convex Area Functionals - Revisited
TLDR
Two new functionals are introduced within the context of the variational grid generation problem: an area functional and a smoothness functional based on an improved adaptive algorithm which focuses on the most folded grid cells.
ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD
The finite element procedure consists in finding an approximate solution in the form of piecewise linear functions, piecewise quadratic, etc. For two-dimensional problems, one of the most frequently
...
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