Adaptive mesh coarsening for quadrilateral and hexahedral meshes

Shepherd, Jason F.; Dewey, Mark W.; Woodbury, Adam C.; Benzley, Steven E.; Staten, Matthew L.; Owen, Steven J.

doi:10.1016/j.finel.2009.06.024

Cited by 35 publications

(16 citation statements)

References 28 publications

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“…We selected a commonly used mesh quality measure, scaled Jacobian [26], to quantify the resulting mesh quality. The scaled Jacobian is the minimum determinant of the Jacobian matrix evaluated at each corner and the center of an element, divided by the corresponding edge lengths [27].…”

Section: Methodsmentioning

confidence: 99%

“…Elements are preferred to have scaled Jacobian values close to 1.0 for the best accuracy in analysis (>0.6 in practice). Values between 0.0 and 0.2 are considered poor because they may result in questionable accuracy in FE analysis in the corresponding regions [26]. For this study, we defined mesh quality to be satisfactory when at least 95% of the elements had a scaled Jacobian greater than 0.6.…”

Section: Methodsmentioning

confidence: 99%

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Automated subject-specific, hexahedral mesh generation via image registration

Ford²,

Greenwald

et al. 2011

Finite Elements in Analysis and Design

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Generating subject-specific, all-hexahedral meshes for finite element analysis continues to be of significant interest in biomechanical research communities. To date, most automated methods “morph” an existing atlas mesh to match with a subject anatomy, which usually result in degradation in mesh quality because of mesh distortion. We present an automated meshing technique that produces satisfactory mesh quality and accuracy without mesh repair. An atlas mesh is first developed using a script. A subject-specific mesh is generated with the same script after transforming the geometry into the atlas space following rigid image registration, and is transformed back into the subject space. By meshing the brain in 11 subjects, we demonstrate that the technique’s performance is satisfactory in terms of both mesh quality (99.5% of elements had a scaled Jacobian >0.6 while <0.01% were between 0 and 0.2) and accuracy (average distance between mesh boundary and geometrical surface was 0.07 mm while <1% greater than 0.5mm). The combined computational cost for image registration and meshing was <4 min. Our results suggest that the technique is effective for generating subject-specific, all-hexahedral meshes and that it may be useful for meshing a variety of anatomical structures across different biomechanical research fields.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Automated subject-specific, hexahedral mesh generation via image registration

Ford²,

Greenwald

et al. 2011

Finite Elements in Analysis and Design

View full text Add to dashboard Cite

show abstract

“…A naive approach is to project the new vertices onto all of the faces of the input mesh with the minimal distance (Hoppe, et al, 1993), which may produce some fold-overs triangles if the points are too far away from the surface. However, in practice the projection operator can be stabilized by constraining the movement of the points on their tangent planes (Remacle, et al, 2012;Shepherd, et al, 2010). Although no theoretical guarantees can be provided, this makes sure that the points do not move too far away from the surface, such that the projection can be safely evaluated.…”

Section: Implementing Aeap Mannermentioning

confidence: 99%

As-equilateral-as-possible surface remeshing

Jin

Tong

2015

JAMDSM

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Surface remeshing aims to produce a high-quality mesh from a given input mesh. In this paper, we present a practical approach to isotropic surface remeshing of triangular meshes in an as-equilateral-as-possible (AEAP) manner. The proposed approach iterates in a two-step manner. In the first step, we optimize the mesh connectivity to reduce the number of irregular vertices. And in the second step, we improve the elements' shape by locally fitting an equilateral triangle separately and globally stitching them to a new mesh with feature constraints. The proposed approach can be effectively used in preprocessing for finite element computations. Experiments are presented to show that our approach is simple and robust, and the remeshed results generate more well-shaped triangles and preserve the features of the original surface, which are favored in many applications.

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“…Note that with the proposed techniques, we do not modify the elements on the previous level. In this sense, we could use general-purpose techniques to modify the current hexahedral mesh [41][42][43]. However, with our template based approach (specific-purpose) we explicitly determine the desired mesh.…”

Section: Related Workmentioning

confidence: 99%

The receding front method applied to hexahedral mesh generation of exterior domains

Ruiz‐Gironés

Roca

Sarrate

2011

Engineering with Computers

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Two of the most successful methods to generate unstructured hexahedral meshes are the grid-based methods and the advancing front methods. On the one hand, the grid-based methods generate high-quality hexahedra in the inner part of the domain using an inside-outside approach. On the other hand, advancing front methods generate highquality hexahedra near the boundary using an outside-inside approach. To combine the advantages of both methodologies, we extend the receding front method: an inside-outside mesh generation approach by means of a reversed advancing front. We apply this approach to generate unstructured hexahedral meshes of exterior domains. To reproduce the shape of the boundaries, we first pre-compute the mesh fronts by combining two solutions of the Eikonal equation on a tetrahedral reference mesh. Then, to generate high-quality elements, we expand the quadrilateral surface mesh of the inner body towards the unmeshed external boundary using the pre-computed fronts as a guide.

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Adaptive mesh coarsening for quadrilateral and hexahedral meshes

Cited by 35 publications

References 28 publications

Automated subject-specific, hexahedral mesh generation via image registration

Automated subject-specific, hexahedral mesh generation via image registration

As-equilateral-as-possible surface remeshing

The receding front method applied to hexahedral mesh generation of exterior domains

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