## Polyhedral Mesh Optimization Using the Interpolation Tensor

Venue: | Proceedings ot the 9th International Meshing Roundtable ‘2000 |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Paoletti_polyhedralmesh,

author = {Stefano Paoletti},

title = {Polyhedral Mesh Optimization Using the Interpolation Tensor},

booktitle = {Proceedings ot the 9th International Meshing Roundtable ‘2000},

year = {},

pages = {19--28}

}

### OpenURL

### Abstract

A method for improving the quality of general conformal polygonal and polyhedral meshes is presented. The method is based on local optimization of a cell quality function that can be derived from the inertia tensor of the arrangement of nodes that belong to the cell. A definition of global mesh quality is also presented as a function of the quality of the cells in the mesh. The cell quality function is related to the ability of the arrangement of points to correctly interpolate test fields.

### Citations

62 | On Combining Laplacian and Optimization-Based Mesh Smoothing Techniques
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(Show Context)
Citation Context ...ally used as cells both by finite element and by finite volume solvers, namely triangles and quadrilaterals in 2D and tetrahedra, prisms, pyramids and hexahedra in 3D. Several researchers [2],[3],[4],=-=[5]-=-,[6],[7],[8] have concentrated their efforts to provide methods to improve the quality of meshes that include such shapes. The inspiring work of P.Knupp [2][3] based on the properties of the metric te... |

54 |
Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities
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(Show Context)
Citation Context ...een historically used as cells both by finite element and by finite volume solvers, namely triangles and quadrilaterals in 2D and tetrahedra, prisms, pyramids and hexahedra in 3D. Several researchers =-=[2]-=-,[3],[4],[5],[6],[7],[8] have concentrated their efforts to provide methods to improve the quality of meshes that include such shapes. The inspiring work of P.Knupp [2][3] based on the properties of t... |

20 | Matrix norms and the condition number: A general framework to improve mesh quality via node-movement - Knupp - 1999 |

15 |
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- 1988
(Show Context)
Citation Context ...f the area of the triangle formed with points p0, p1 and p 2. The condition number of A, in this case, would read as: 2 2 2 2 ( L1 + L2 ) 2 I1 k = − 2 = − 2 I 4a 2 that is the so-called Oddy’s metric =-=[11]-=-, which is widely used to improve triangular and quadrilateral meshes. If we apply the same formulation to the triangle of edges L 1, L 2, L3 and area a the result is: 2 2 2 2 2 ( L1 + L2 + L3 ) 2 I1 ... |

14 |
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(Show Context)
Citation Context ...is clearly invariant under rotation, translation, reflection and uniform scaling, so it meets the basic requirements for a cell shape measure that have been outlined for tetrahedral shape measures in =-=[10]-=-. This definition of cell quality has values between 0 and 1 where 1 stands for a perfect cell and 0 for a degenerated one. The above definition holds in any dimension. Obviously, practical applicatio... |

13 | A comparison of triangle quality measures
- Pebay, Baker
- 2001
(Show Context)
Citation Context ...angle of edges L 1, L 2, L3 and area a the result is: 2 2 2 2 2 ( L1 + L2 + L3 ) 2 I1 k = − 2 = − 2 I 12a 2sthat substantially equals the square of the matrix-normbased triangle quality measure k2 in =-=[12]-=-. 4.MESH QUALITY It is not completely clear which is the best way to define the quality Q of a mesh, starting from the quality qi (i=1,..,N) of the N component cells. One could define such quality in ... |

7 | hp-Meshless cloud method
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(Show Context)
Citation Context ...index of a point and: i = 1, 2, 3 j = 1, 2, 3 x = x, x = y, x = z 1 ∆ϕ ∆x ( k ) ( k ) i 2 = ϕ( p ) −ϕ ( p ) k = x ( p ) − x ( p ) i This methodology has also been called Generalized Finite Difference =-=[9]-=- and is the simplest definition used by meshless techniques. When the Taylor series is truncated at the second order terms, the least square method depicted above may be actually used to generate the ... |

4 |
A discrete variational method
- Castillo
- 1991
(Show Context)
Citation Context ...d as cells both by finite element and by finite volume solvers, namely triangles and quadrilaterals in 2D and tetrahedra, prisms, pyramids and hexahedra in 3D. Several researchers [2],[3],[4],[5],[6],=-=[7]-=-,[8] have concentrated their efforts to provide methods to improve the quality of meshes that include such shapes. The inspiring work of P.Knupp [2][3] based on the properties of the metric tensor der... |

1 | Polyhedral mesh generation
- Oaks, Paoletti
- 2000
(Show Context)
Citation Context ...red field. Polyhedral meshes have started to be available only recently, with the introduction of reliable face-based finite volume methods and related polyhedral mesh generators in the CFD community =-=[1]-=-. However, polyhedral meshes can be trivially generated starting from a tetrahedral mesh and creating the dual mesh, i.e. the Voronoi or Dirichlet mesh. Dual meshes created from tetrahedral meshes hav... |

1 |
Practical Optimization-Based Smoothing of Tetrahedral Meshes
- Paoletti
(Show Context)
Citation Context ... cells both by finite element and by finite volume solvers, namely triangles and quadrilaterals in 2D and tetrahedra, prisms, pyramids and hexahedra in 3D. Several researchers [2],[3],[4],[5],[6],[7],=-=[8]-=- have concentrated their efforts to provide methods to improve the quality of meshes that include such shapes. The inspiring work of P.Knupp [2][3] based on the properties of the metric tensor derived... |