2,787 research outputs found
A Density Control Based Adaptive Hexahedral Mesh Generation Algorithm
A density control based adaptive hexahedral mesh generation algorithm for three dimensional models is presented in this paper. The first step of this algorithm is to identify the characteristic boundary of the solid model which needs to be meshed. Secondly, the refinement fields are constructed and modified according to the conformal refinement templates, and used as a metric to generate an initial grid structure. Thirdly, a jagged core mesh is generated by removing all the elements in the exterior of the solid model. Fourthly, all of the surface nodes of the jagged core mesh are matching to the surfaces of the model through a node projection process. Finally, the mesh quality such as topology and shape is improved by using corresponding optimization techniques
Linear Complexity Hexahedral Mesh Generation
We show that any polyhedron forming a topological ball with an even number of
quadrilateral sides can be partitioned into O(n) topological cubes, meeting
face to face. The result generalizes to non-simply-connected polyhedra
satisfying an additional bipartiteness condition. The same techniques can also
be used to reduce the geometric version of the hexahedral mesh generation
problem to a finite case analysis amenable to machine solution.Comment: 12 pages, 17 figures. A preliminary version of this paper appeared at
the 12th ACM Symp. on Computational Geometry. This is the final version, and
will appear in a special issue of Computational Geometry: Theory and
Applications for papers from SCG '9
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
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational
geometry is presented.Comment: 7 pages; 72 reference
Orbital and Maxillofacial Computer Aided Surgery: Patient-Specific Finite Element Models To Predict Surgical Outcomes
This paper addresses an important issue raised for the clinical relevance of
Computer-Assisted Surgical applications, namely the methodology used to
automatically build patient-specific Finite Element (FE) models of anatomical
structures. From this perspective, a method is proposed, based on a technique
called the Mesh-Matching method, followed by a process that corrects mesh
irregularities. The Mesh-Matching algorithm generates patient-specific volume
meshes from an existing generic model. The mesh regularization process is based
on the Jacobian matrix transform related to the FE reference element and the
current element. This method for generating patient-specific FE models is first
applied to Computer-Assisted maxillofacial surgery, and more precisely to the
FE elastic modelling of patient facial soft tissues. For each patient, the
planned bone osteotomies (mandible, maxilla, chin) are used as boundary
conditions to deform the FE face model, in order to predict the aesthetic
outcome of the surgery. Seven FE patient-specific models were successfully
generated by our method. For one patient, the prediction of the FE model is
qualitatively compared with the patient's post-operative appearance, measured
from a Computer Tomography scan. Then, our methodology is applied to
Computer-Assisted orbital surgery. It is, therefore, evaluated for the
generation of eleven patient-specific FE poroelastic models of the orbital soft
tissues. These models are used to predict the consequences of the surgical
decompression of the orbit. More precisely, an average law is extrapolated from
the simulations carried out for each patient model. This law links the size of
the osteotomy (i.e. the surgical gesture) and the backward displacement of the
eyeball (the consequence of the surgical gesture)
Unstructured and semi-structured hexahedral mesh generation methods
Discretization techniques such as the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in ap- plied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to gener- ate. However, in many applications such as boundary layers in computational fluid dy- namics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.Peer ReviewedPostprint (published version
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