Hexahedral-dominant meshing

This article introduces a method that generates a hexahedral-dominant mesh from an input tetrahedral mesh.It follows a three-steps pipeline similar to the one proposed by Carrier-Baudoin et al.:(1) generate a frame field; (2) generate a pointset P that is mostly organized on a regulargrid locally aligned with the frame field; and (3) generate thehexahedral-dominant mesh by recombining the tetrahedra obtained from the constrained Delaunay triangulation of P.For step (1), we use a state of the art algorithm to generate a smooth frame field. For step (2), weintroduce an extension of Periodic Global Parameterization to the volumetric case. As compared withother global parameterization methods (such as CubeCover), our method relaxes some global constraintsand avoids creating degenerate elements, at the expense of introducing some singularities that aremeshed using non-hexahedral elements. For step (3), we build on the formalism introduced byMeshkat and Talmor, fill-in a gap in their proof and provide a complete enumeration of all thepossible recombinations, as well as an algorithm that efficiently detects all the matches in a tetrahedral mesh.The method is evaluated and compared with the state of the art on adatabase of examples with various mesh complexities, varying fromacademic examples to real industrial cases. Compared with the methodof Carrier-Baudoin et al., the method results in better scoresfor classical quality criteria of hexahedral-dominant meshes(hexahedral proportion, scaled Jacobian, etc.). The methodalso shows better robustness than CubeCover and its derivativeswhen applied to complicated industrial models

Decomposing complex thin-walled CAD models for hexahedral-dominant meshing

AbstractThis paper describes an automatic method for identifying thin-sheet regions (regions with large lateral dimensions relative to the thickness) for complex thin walled components, with a view to using this information to guide the hex meshing process. This fully automated method has been implemented in a commercial CAD system (Siemens NX) and is based on the interrogation and manipulation of face pairs, which are sets of opposing faces bounding thin-sheet regions. Careful consideration is given to the mapping, merging and intersection of face pairs to generate topologies suitable for sweep meshing thin-sheet regions, and for treating the junctions between adjacent thin-sheet regions. The quality of the resulting hexahedral mesh is considered when making decisions on the generation and positioning of the cutting surfaces required to isolate thin-sheet regions. The resulting decomposition delivers a substantial step towards automatic hexahedral meshing for complex thin-walled geometries. It is proposed that hexahedral meshes be applied to the identified thin-sheet regions by quad meshing one of the faces bounding the thin-sheet region and sweeping it through the thickness to create hexahedral elements

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

Low-order continuous finite element spaces on hybrid non-conforming hexahedral-tetrahedral meshes

This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to two triangular faces of tetrahedra. We introduce a set of low-order continuous (C0) finite element spaces defined on these meshes. They are built from standard tri-linear and quadratic Lagrange finite elements with an extra set of constraints at non-conforming hexahedra-tetrahedra junctions to recover continuity. We consider both the continuity of the geometry and the continuity of the function basis as follows: the continuity of the geometry is achieved by using quadratic mappings for tetrahedra connected to tri-affine hexahedra and the continuity of interpolating functions is enforced in a similar manner by using quadratic Lagrange basis on tetrahedra with constraints at non-conforming junctions to match tri-linear hexahedra. The so-defined function spaces are validated numerically on simple Poisson and linear elasticity problems for which an analytical solution is known. We observe that using a hybrid mesh with the proposed function spaces results in an accuracy significantly better than when using linear tetrahedra and slightly worse than when solely using tri-linear hexahedra. As a consequence, the proposed function spaces may be a promising alternative for complex geometries that are out of reach of existing full hexahedral meshing methods

Optimal Design of V-Shaped Fin Heat Sink for Active Antenna Unit of 5G Base Station

The active antenna unit (AAU) is one of the main parts of the 5G base station, which has a large size and a high density of chipsets, and operates at a significantly high temperature. This systematic study presents an optimal design for the heat sink of an AAU with a V-shaped fin arrangement. First, a simulation of the heat dissipation was conducted on two designs of the heat sink – in-line and V-shaped fins – which was validated by experimental results. The result shows that the heat sink with V-shaped fins performed better compared to conventional models such as heat sinks with in-line fins. Secondly, computational fluid dynamics (CFD) and the Lagrange interpolation method were applied to find out an optimal set of design parameters for the heat sink. It is worth noting that the optimal parameters of the orientation angle and fin spacing considerably affected the heat sink’s performance.  

Optimal Design of V-Shaped Fin Heat Sink for Active Antenna Unit of 5G Base Station

The active antenna unit (AAU) is one of the main parts of the 5G base station, which has a large size and a high density of chipsets, and operates at a significantly high temperature. This systematic study presents an optimal design for the heat sink of an AAU with a V-shaped fin arrangement. First, a simulation of the heat dissipation was conducted on two designs of the heat sink – in-line and V-shaped fins – which was validated by experimental results. The result shows that the heat sink with V-shaped fins performed better compared to conventional models such as heat sinks with in-line fins. Secondly, computational fluid dynamics (CFD) and the Lagrange interpolation method were applied to find out an optimal set of design parameters for the heat sink. It is worth noting that the optimal parameters of the orientation angle and fin spacing considerably affected the heat sink’s performance.  

Multi-Modal Framework for Subject-Specific Finite Element Modeling of the Buttocks

International audienceIn order to produce high quality personalized FE models, it is necessary to resort to medical imaging and acquire the most relevant possible description of the modeled morphology. Yet building a FE model from a medical data set can be a challenging and time consuming task. To overcome the commonly encountered problems, this paper introduces a "mesh warping" approach chosen for its versatility. A biomechanical finite element model of the buttocks soft tissues is generated for an efficient prevention of pressure ulcers

Multi-modal framework for subject-specific finite element model generation aimed at pressure ulcer prevention.

International audienceThis study outlines a methodology aiming at the definition of an individual and personalised pressure ulcer risk assessment scale based on patient-specific biomechanical modellin