There are 174 Subdivisions of the Hexahedron into Tetrahedra

This article answers an important theoretical question: How many different subdivisions of the hexahedron into tetrahedra are there? It is well known that the cube has five subdivisions into 6 tetrahedra and one subdivision into 5 tetrahedra. However, all hexahedra are not cubes and moving the vertex positions increases the number of subdivisions. Recent hexahedral dominant meshing methods try to take these configurations into account for combining tetrahedra into hexahedra, but fail to enumerate them all: they use only a set of 10 subdivisions among the 174 we found in this article. The enumeration of these 174 subdivisions of the hexahedron into tetrahedra is our combinatorial result. Each of the 174 subdivisions has between 5 and 15 tetrahedra and is actually a class of 2 to 48 equivalent instances which are identical up to vertex relabeling. We further show that exactly 171 of these subdivisions have a geometrical realization, i.e. there exist coordinates of the eight hexahedron vertices in a three-dimensional space such that the geometrical tetrahedral mesh is valid. We exhibit the tetrahedral meshes for these configurations and show in particular subdivisions of hexahedra with 15 tetrahedra that have a strictly positive Jacobian

Identifying combinations of tetrahedra into hexahedra: a vertex based strategy

Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh T into hexahedra, prisms, or pyramids. All identified cells are valid for engineering analysis. First, all combinations of eight/six/five vertices whose connectivity in T matches the connectivity of a hexahedron/prism/pyramid are computed. The subset of tetrahedra of T triangulating each potential cell is then determined. Quality checks allow to early discard poor quality cells and to dramatically improve the efficiency of the method. Each potential hexahedron/prism/pyramid is computed only once. Around 3 millions potential hexahedra are computed in 10 seconds on a laptop. We finally demonstrate that the set of potential hexes built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements.Comment: Preprint submitted to CAD (26th IMR special issue

GPU-accelerated discontinuous Galerkin methods on hybrid meshes

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.Comment: Submitted to CMAM

Stress-Induced Premature Senescence or Stress-Induced Senescence-Like Phenotype: One In Vivo

No consensus exists so far on the definition of cellular senescence. The narrowest definition of senescence is irreversible growth arrest triggered by telomere shortening counting cell generations (definition 1). Other authors gave an enlarged functional definition encompassing any kind of irreversible arrest of proliferative cell types induced by damaging agents or cell cycle deregulations after overexpression of proto-oncogenes (definition 2). As stress increases, the proportion of cells in “stress-induced premature senescence-like phenotype” according to definition 1 or “stress-induced premature senescence,” according to definition 2, should increase when a culture reaches growth arrest, and the proportion of cells that reached telomere-dependent replicative senescence due to the end-replication problem should decrease. Stress-induced premature senescence-like phenotype and telomere-dependent replicatively senescent cells share basic similarities such as irreversible growth arrest and resistance to apoptosis, which may appear through different pathways. Irreversible growth arrest after exposure to oxidative stress and generation of DNA damage could be as efficient in avoiding immortalisation as “telomere-dependent” replicative senescence. Probabilities are higher that the senescent cells (according to definition 2) appearing in vivo are in stress-induced premature senescence rather than in telomere-dependent replicative senescence. Examples are given suggesting these cells affect in vivo tissue (patho)physiology and aging

Efficient Generation of High-Order Boundary Layer Meshes

International audienc

Modèle en éléments finis de mélange fluide/grains

International audienceUn modèle de mélange fluide/grains est présenté. Pour la phase granulaire, la dynamique des contacts est calculée à l'échelle des grains. À une échelle supérieure, les équations de Navier-Stokes/Brinkman modélisent l'écoulement du fluide dans un milieu poreux. Ces équations sont résolues au moyen d'une méthode éléments finis. Cette approche permet de simuler dans un même modèle une transition continue entre, à concentration élevée de grains, un régime de Darcy et, à faible concentration, un écoulement fluide classique

Cardiovascular and lung mesh generation based on centerlines

We present a fully automatic procedure for the mesh generation of tubular geometries such as blood vessels or airways. The procedure is implemented in the open-source Gmsh software and relies on a centerline description of the input geometry. The presented method can generate different type of meshes: isotropic tetrahedral meshes, anisotropic tetrahedral meshes, and mixed hexahedral/tetrahedral meshes. Additionally, a multiple layered arterial wall can be generated with a variable thickness. All the generated meshes rely on a mesh size field and a mesh metric that is based on centerline descriptions, namely the distance to the centerlines and a local reference system based on the tangent and the normal directions to the centerlines. Different examples show that the proposed method is very efficient and robust and leads to high quality computational meshes. Copyright © 2013 John Wiley & Sons, Ltd

Generation of Curvilinear Meshes with Appropriate Geometrical and Numerical Properties

International audienc

Geometrical accuracy and numerical properties of high-order meshes

International audienc