New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation
In this paper, we review some grid quality metrics and define some new quality measures for quadrilateral elements. The curved elements are not discussed. Usually, the maximum value of a quality measure corresponds to the minimum value of the energy density over the grid. We also define new discrete...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/28/5/95 |
| _version_ | 1797573086824890368 |
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| author | Guilmer Ferdinand González Flores Pablo Barrera Sánchez |
| author_facet | Guilmer Ferdinand González Flores Pablo Barrera Sánchez |
| author_sort | Guilmer Ferdinand González Flores |
| collection | DOAJ |
| description | In this paper, we review some grid quality metrics and define some new quality measures for quadrilateral elements. The curved elements are not discussed. Usually, the maximum value of a quality measure corresponds to the minimum value of the energy density over the grid. 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 to preserve convex grid cells in each step of the optimization process. |
| first_indexed | 2024-03-10T21:04:41Z |
| format | Article |
| id | doaj.art-60334555a66c49a0a27a40a62bca13db |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T21:04:41Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-60334555a66c49a0a27a40a62bca13db2023-11-19T17:15:37ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472023-09-012859510.3390/mca28050095New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid GenerationGuilmer Ferdinand González Flores0Pablo Barrera Sánchez1Department of Mathematics, Faculty of Sciences, National Autonomous University of Mexico, Mexico City 04510, MexicoDepartment of Mathematics, Faculty of Sciences, National Autonomous University of Mexico, Mexico City 04510, MexicoIn this paper, we review some grid quality metrics and define some new quality measures for quadrilateral elements. The curved elements are not discussed. Usually, the maximum value of a quality measure corresponds to the minimum value of the energy density over the grid. 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 to preserve convex grid cells in each step of the optimization process.https://www.mdpi.com/2297-8747/28/5/95mesh generationquality measureaspect ratioquality improvement |
| spellingShingle | Guilmer Ferdinand González Flores Pablo Barrera Sánchez New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation Mathematical and Computational Applications mesh generation quality measure aspect ratio quality improvement |
| title | New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation |
| title_full | New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation |
| title_fullStr | New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation |
| title_full_unstemmed | New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation |
| title_short | New Quality Measures for Quadrilaterals and New Discrete Functionals for Grid Generation |
| title_sort | new quality measures for quadrilaterals and new discrete functionals for grid generation |
| topic | mesh generation quality measure aspect ratio quality improvement |
| url | https://www.mdpi.com/2297-8747/28/5/95 |
| work_keys_str_mv | AT guilmerferdinandgonzalezflores newqualitymeasuresforquadrilateralsandnewdiscretefunctionalsforgridgeneration AT pablobarrerasanchez newqualitymeasuresforquadrilateralsandnewdiscretefunctionalsforgridgeneration |