395 research outputs found
A case study in hexahedral mesh generation: Simulation of the human mandible
We provide a case study for the generation of pure hexahedral meshes for the numerical simulation of physiological stress scenarios of the human mandible. Due to its complex and very detailed free-form geometry, the mandible model is very demanding. This test case is used as a running example to demonstrate the applicability of a combinatorial approach for the generation of hexahedral meshes by means of successive dual cycle eliminations, which has been proposed by the second author in previous work. We report on the progress and recent advances of the cycle elimination scheme. The given input data, a surface triangulation obtained from computed tomography data, requires a substantial mesh reduction and a suitable conversion into a quadrilateral surface mesh as a first step, for which we use mesh clustering and b-matching techniques. Several strategies for improved cycle elimination orders are proposed. They lead to a significant reduction in the mesh size and a better structural quality. Based on the resulting combinatorial meshes, gradient-based optimized smoothing with the condition number of the Jacobian matrix as objective together with mesh untangling techniques yielded embeddings of a satisfactory quality. To test our hexahedral meshes for the mandible model within an FEM simulation we used the scenario of a bite on a ‘hard nut.’ Our simulation results are in good agreement with observations from biomechanical experiments
Finding Hexahedrizations for Small Quadrangulations of the Sphere
This paper tackles the challenging problem of constrained hexahedral meshing.
An algorithm is introduced to build combinatorial hexahedral meshes whose
boundary facets exactly match a given quadrangulation of the topological
sphere. This algorithm is the first practical solution to the problem. It is
able to compute small hexahedral meshes of quadrangulations for which the
previously known best solutions could only be built by hand or contained
thousands of hexahedra. These challenging quadrangulations include the
boundaries of transition templates that are critical for the success of general
hexahedral meshing algorithms.
The algorithm proposed in this paper is dedicated to building combinatorial
hexahedral meshes of small quadrangulations and ignores the geometrical
problem. The key idea of the method is to exploit the equivalence between quad
flips in the boundary and the insertion of hexahedra glued to this boundary.
The tree of all sequences of flipping operations is explored, searching for a
path that transforms the input quadrangulation Q into a new quadrangulation for
which a hexahedral mesh is known. When a small hexahedral mesh exists, a
sequence transforming Q into the boundary of a cube is found; otherwise, a set
of pre-computed hexahedral meshes is used.
A novel approach to deal with the large number of problem symmetries is
proposed. Combined with an efficient backtracking search, it allows small
shellable hexahedral meshes to be found for all even quadrangulations with up
to 20 quadrangles. All 54,943 such quadrangulations were meshed using no more
than 72 hexahedra. This algorithm is also used to find a construction to fill
arbitrary domains, thereby proving that any ball-shaped domain bounded by n
quadrangles can be meshed with no more than 78 n hexahedra. This very
significantly lowers the previous upper bound of 5396 n.Comment: Accepted for SIGGRAPH 201
Flipping Cubical Meshes
We define and examine flip operations for quadrilateral and hexahedral
meshes, similar to the flipping transformations previously used in triangular
and tetrahedral mesh generation.Comment: 20 pages, 24 figures. Expanded journal version of paper from 10th
International Meshing Roundtable. This version removes some unwanted
paragraph breaks from the previous version; the text is unchange
All‐hexahedral element meshing: automatic elimination of self‐intersecting dual lines
There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied. 
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
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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7th International Meshing Roundtable '98
The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries
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Numerical and experimental modelling of microwave applicators
This thesis presents a time domain finite element method for the solution of microwave
heating problems. This is the first time that this particular technique has been applied
to microwave heating. It is found that the standard frequency domain finite element
method is unsuitable for analysing multimode applicators containing food-like materials
due to a severe ill-conditioning of the matrix equations. The field distribution in multimode
applicators loaded with low loss materials is found to be very sensitive to small
frequency changes. Several solutions at different frequencies are therefore required to
characterise the behaviour of the loaded applicator. The time domain finite element
method is capable of producing multiple solutions at different frequencies when used
with Gaussian pulse excitation; it is therefore ideally suited to the analysis of multimode
applicators. A brief survey of the methods available for the solution of the linear
equations is provided. The performance of these techniques with both the frequency
domain and time domain finite element methods is then studied.
Single mode applicators are also analysed and it is found that the frequency domain
method is superior in these cases. Comparisons are given between the calculated results
and experimental data for both single mode and multimode systems. The importance
of experimental verification being stressed.
The choice of element type is an important consideration for the finite element
method. Three basic types of element are considered; nodal, Whitney edge elements
and linear edge elements. Comparisons of the errors with these elements show that
Whitney elements produce a consistently lower error when post-processing is used to
smooth the solution.
The coupled thermal-electromagnetic problem is investigated with many difficulties
being identified for the application to multimode cavity problems
ICASE/LaRC Workshop on Adaptive Grid Methods
Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field
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