Non-degeneracy study of the 8-tetrahedra longest-edge partition

Plaza, Ángel; Padrón, Miguel A.; Suárez, José P.

doi:10.1016/j.apnum.2004.12.003

Cited by 21 publications

(15 citation statements)

References 16 publications

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“…Much work has been spent on this topic, see, e.g. [1][2][3][4][7][8][9][12][13][14]16]. The present article closes a gap by proving stability (i.e.…”

Section: Introductionmentioning

confidence: 91%

“…For a review about different shape quality measures for tetrahedra, we refer to Liu and Joe [8], Plaza et al [12], and the references in the latter one.…”

Section: Shape Quality Measurement and Stabilitymentioning

confidence: 99%

“…We call this the 8-tetrahedra longest-edge (8Te-LE) partition. Plaza et al [12] have made numerical experiments with this partitioning method that lead to the suggestion that this method is strongly stable (with respect to η) with c ≈ 0.3155. Recently, Plaza [11] showed strong stability with c = 1 for a special kind of tetrahedra that occur when a hexahedral grid is transformed to a tetrahedral grid using so-called Kuhn-type triangulations.…”

Section: Partition Of Tetrahedramentioning

confidence: 99%

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Stability of the 8-tetrahedra shortest-interior-edge partitioning method

Kröger

Preußer

2008

Numer. Math.

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We consider a tetrahedron partitioning method, known in the literature as the 8-tetrahedra shortest-interior-edge partition. For this method, which is a variant of Freudenthal's algorithm in three space dimensions, we prove that the infinite series of refined meshes (for any given initial mesh) is stable in the sense that the degree of degeneracy of the cells remains bounded. We give an explicit estimate in terms of a standard shape quality measure introduced by Liu and Joe. Furthermore, we show that our estimate is sharp. The estimate also holds for Freudenthal's algorithm (in three space dimensions) provided that it is initialized appropriately. Numerical experiments confirm our result as well as its sharpness.

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“…Much work has been spent on this topic, see, e.g. [1][2][3][4][7][8][9][12][13][14]16]. The present article closes a gap by proving stability (i.e.…”

Section: Introductionmentioning

confidence: 91%

“…For a review about different shape quality measures for tetrahedra, we refer to Liu and Joe [8], Plaza et al [12], and the references in the latter one.…”

Section: Shape Quality Measurement and Stabilitymentioning

confidence: 99%

Section: Partition Of Tetrahedramentioning

confidence: 99%

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Stability of the 8-tetrahedra shortest-interior-edge partitioning method

Kröger

Preußer

2008

Numer. Math.

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“…Several regularity criteria for triangular and tetrahedral finite element partitions have been proposed in literature [5,16,20]. Also, in several triangle partitions properties on mesh quality improvement have been studied [15,21].…”

Section: Introductionmentioning

confidence: 99%

Properties of triangulations obtained by the longest-edge bisection

Perdomo

Plaza

2014

Open Mathematics

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Abstract:The Longest-Edge (LE) bisection of a triangle is obtained by joining the midpoint of its longest edge with the opposite vertex. Here two properties of the longest-edge bisection scheme for triangles are proved. For any triangle, the number of distinct triangles (up to similarity) generated by longest-edge bisection is finite. In addition, if LE-bisection is iteratively applied to an initial triangle, then minimum angle of the resulting triangles is greater or equal than a half of the minimum angle of the initial angle. The novelty of the proofs is the use of an hyperbolic metric in a shape space for triangles. MSC:51M09, 65M50, 65N50

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“…The structured element splitting allows for a good control of the newly created elements. Depending on the non-structured element splitting strategy used to refine the mesh, one can obtain more distorted elements or elements of an increasing geometrical quality [12,13].…”

Section: Introductionmentioning

confidence: 99%

A hierarchical h adaptivity methodology based on element subdivision

Ródenas

Albelda

Tur

et al. 2017

revuin

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Este artículo puede compartirse bajo la licencia CC BY-ND 4.0 y se referencia usando el siguiente formato: J.J. Ródenas, J.Albelda, M. Tur, F.J. Fuenmayor, "A hierarchical h adaptivity methodology based on element subdivision", UIS Ingenierías, vol. 16, no. ABSTRACTThis paper presents a hierarchical h adaptive methodology for Finite Element Analysis based on the hierarchical relations between parent and child elements that come out if these elements are geometrically similar. Under this similarity condition the terms involved in the evaluation of element stiffness matrices of parent and child elements are related by a constant which is a function of the element sizes ratio (scaling factor). These relations have been the basis for the development of a hierarchical h adaptivity methodology based on element subdivision and the use of multipoint-constraints to ensure C 0 continuity. The use of a hierarchical data structure significantly reduces the amount of calculations required for the mesh refinement, the evaluation of the global stiffness matrix, element stresses and element error estimation. The data structure also produces a natural reordering of the global stiffness matrix that improves the behaviour of the Cholesky factorization. KEYWORDS:Adaptive Modelling, Hierarchical properties, Mesh Enrichment, Mesh Generation. RESUMENEn este artículo se presenta una metodología h adaptativa para el Análisis por Elementos Finitos basada en las relaciones jerárquicas entre elementos padre e hijo que surgen si estos elementos son geométricamente similares. Bajo esta condición de similitud, los términos resultantes de la evaluación de las matrices de rigidez de elementos padre e hijo están relacionados por una constante que es una función de la relación de tamaños de elemento (factor de escala). Estas relaciones han sido la base para el desarrollo de una metodología jerárquica h adaptativa basada en la subdivisión de elementos y el uso de restricciones multipunto para asegurar la continuidad C 0 . El uso de una estructura de datos jerárquica reduce significativamente la cantidad de cálculos requeridos para el refinamiento de la malla, la evaluación de la matriz de rigidez global, las tensiones de los elementos y la estimación del error del elemento. La estructura de datos también produce un reordenamiento natural de la matriz de rigidez global que mejora el comportamiento de la factorización de Cholesky. PALABRAS CLAVE:Modelado Adaptativo, Propiedades jerárquicas, Enriquecimiento de malla, Mallado.

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Non-degeneracy study of the 8-tetrahedra longest-edge partition

Cited by 21 publications

References 16 publications

Stability of the 8-tetrahedra shortest-interior-edge partitioning method

Stability of the 8-tetrahedra shortest-interior-edge partitioning method

Properties of triangulations obtained by the longest-edge bisection

A hierarchical h adaptivity methodology based on element subdivision

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