A comparison of tetrahedron quality measures

Parthasarathy, V.; Graichen, C. M.; Hathaway, A. F.

doi:10.1016/0168-874x(94)90033-7

Cited by 143 publications

(75 citation statements)

References 4 publications

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“…The measure is defined as V/l rms 3 , with V the volume of the tetrahedron and l rms the root mean square of the edge lengths [4,20]. The value 1 corresponds to a perfectly regular tetrahedron.…”

Section: Resultsmentioning

confidence: 99%

Efficient tetrahedral remeshing of feature models for finite element analysis

Smit

Bronsvoort

2009

Engineering with Computers

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Finite element analysis is nowadays widely used for product testing. At various moments during the design phase, aspects of the physical behaviour of the product are simulated by performing an analysis of the model. For each analysis, a mesh needs to be created that represents the geometry of the model at that point. In particular during the later stages of the development cycle, often only minor modifications are made to a model between design iterations. In that case it can be beneficial to reuse part of the previous mesh, especially if it was costly to construct. A new method is presented that efficiently constructs a tetrahedral mesh based on a tetrahedral mesh of a feature model at an earlier point of the design cycle. This is done by analysing the difference of the two feature models from the point of view of the individual features. By this means we can find a natural correspondence between the geometries of the feature models, and relate this to the mesh of the earlier model. We discuss the algorithm, gained improvements, quality of the results, and conditions for this method to be effective.

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Section: Resultsmentioning

confidence: 99%

Efficient tetrahedral remeshing of feature models for finite element analysis

Smit

Bronsvoort

2009

Engineering with Computers

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“…These measures will deÿne a threshold used to determine if an element is considered ill-shaped. This issue is well represented in the literature [5,[9][10][11][12][13][14], with measures of all kinds. Considering that, in 3D, it is more di cult to ensure that high-quality meshes are generated, the examples shown are three-dimensional ones, in order to attest the e ciency of the proposed technique.…”

Section: Quality Measuresmentioning

confidence: 99%

“…The range of valid values varies from [1; ∞) [5,11], and the optimal value for the regular tetrahedron is approximately 8.5. For each element, this metric is evaluated and, if it is outside a predeÿned range, the element is classiÿed as ill-shaped.…”

Section: Quality Measuresmentioning

confidence: 99%

A back-tracking procedure for optimization of simplex meshes

Cavalcante-Neto

Martha

Wawrzynek

et al. 2005

Commun. Numer. Meth. Engng.

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SUMMARYThis work presents a back-tracking procedure for the optimization of meshes. It can be applied to all ill-shaped elements in a mesh in order to improve quality in mesh optimization. Basically, the original mesh is reconstructed in regions around the ill-shaped elements by means of a set of deletion and reconstruction operations based on visibility tests. The back-tracking procedure ÿxes problems related to the quality of generated meshes in general and can be applied in two or three dimensions. The procedure works by deleting elements ranked below a predeÿned shape quality measure. It is important to mention that, although the presented procedure was devised for advancing-front algorithms, it can also be used in meshes generated by di erent approaches, such as Delaunay and others, requiring no modiÿcation. The proposed procedure is applicable to simplex elements (triangles and tetrahedra), although ideally it could be extended to other types of elements. Examples of improved meshes using the back-tracking procedure are presented, in which the quality of these meshes is assessed in order to validate the procedure proposed in this work.

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“…The M1 measure is a successful purely geometric measure that serves to bridge the gap with previous efforts in geometric mesh quality analysis [8]. Conversely, M2, M3, and M4 are all theoretically linked to FE approximation accuracy.…”

Section: Theoretical Mesh Quality Indicatorsmentioning

confidence: 99%

Impact of mesh quality improvement systems on the accuracy of adaptive finite-element electromagnetics with tetrahedra

Dorica

Giannacopoulos

2005

IEEE Trans. Magn.

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Finite-element (FE) accuracy can be directly affected by mesh quality. The potential benefits and related costs of a family of new mesh quality improvement systems are investigated using a suite of electromagnetic benchmarks and mesh quality measures theoretically linked to FE accuracy. Experimental findings suggest error reductions on the order of 10% for half-second runtimes.Index Terms-Adaptive systems, electromagnetic analysis, finite-element methods (FEMs), mesh improvement, mesh quality.

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A comparison of tetrahedron quality measures

Cited by 143 publications

References 4 publications

Efficient tetrahedral remeshing of feature models for finite element analysis

Efficient tetrahedral remeshing of feature models for finite element analysis

A back-tracking procedure for optimization of simplex meshes

Impact of mesh quality improvement systems on the accuracy of adaptive finite-element electromagnetics with tetrahedra

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