Optimal Coarsening of Unstructured Meshes

Talmor, Dafna; Teng, Shang‐Hua

doi:10.1006/jagm.1998.0990

Cited by 32 publications

(38 citation statements)

References 11 publications

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“…Miller et al proposed a function-based coarsening method in 2D [6]. Compared with maximal independent set (MIS)-based methods for vertex connectivity graphs, it gives better results.…”

Section: Function-based Coarseningmentioning

confidence: 97%

“…To devise a mesh decimation method for CAE applications, the following additional criteria should be considered: (a) watertightness of the resulting mesh, (b) mesh quality, in terms of element geometric shape and smooth size variation, (c) local curvature on the surface and (d) volume thickness. Several mesh decimation algorithms for CAE applications have been presented in the literature [6,7]. Some of them are limited to 2D models.…”

Section: Introductionmentioning

confidence: 99%

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Robust generation of high‐quality unstructured meshes on realistic biomedical geometry

Ito

Shum

Shih

et al. 2005

Numerical Meth Engineering

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SUMMARYIn this paper, we propose efficient and robust unstructured mesh generation methods based on computed tomography (CT) and magnetic resonance imaging (MRI) data, in order to obtain a patient-specific geometry for high-fidelity numerical simulations. Surface extraction from medical images is carried out mainly using open source libraries, including the Insight Segmentation and Registration Toolkit and the Visualization Toolkit, into the form of facet surface representation. To create high-quality surface meshes, we propose two approaches. One is a direct advancing front method, and the other is a modified decimation method. The former emphasizes the controllability of local mesh density, and the latter enables semi-automated mesh generation from low-quality discrete surfaces. An advancingfront-based volume meshing method is employed. Our approaches are demonstrated with high-fidelity tetrahedral meshes around medical geometries extracted from CT/MRI data.

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“…Miller et al proposed a function-based coarsening method in 2D [6]. Compared with maximal independent set (MIS)-based methods for vertex connectivity graphs, it gives better results.…”

Section: Function-based Coarseningmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Robust generation of high‐quality unstructured meshes on realistic biomedical geometry

Ito

Shum

Shih

et al. 2005

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Recent work by Miller et al [11] provides a remedy. They construct an MIS not of the vertex connectivity graph but of a con ict graph.…”

Section: Selection Of Points To Include In the Coarse Meshmentioning

confidence: 97%

“…Recently, work in mesh generation by bubble packing has produced spin-o s in mesh coarsening. Speciÿcally, Miller et al [11] have shown that the proper criterion for whether two ÿne mesh vertices can both be allowed in the coarse mesh is the distance between them relative to a measure of the mesh length scale at each vertex. They were able to show that using this criterion the quality of the coarse mesh is bounded below for any given ÿne mesh.…”

Section: Introductionmentioning

confidence: 99%

Coarsening unstructured meshes by edge contraction

Ollivier‐Gooch

2003

Numerical Meth Engineering

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SUMMARYA new unstructured mesh coarsening algorithm has been developed for use in conjunction with multilevel methods. The algorithm preserves geometrical and topological features of the domain, and retains a maximal independent set of interior vertices to produce good coarse mesh quality. In anisotropic meshes, vertex selection is designed to retain the structure of the anisotropic mesh while reducing cell aspect ratio. Vertices are removed incrementally by contracting edges to zero length. Each vertex is removed by contracting the edge that maximizes the minimum sine of the dihedral angles of cells a ected by the edge contraction. Rarely, a vertex slated for removal from the mesh cannot be removed; the success rate for vertex removal is typically 99.9% or more.For two-dimensional meshes, both isotropic and anisotropic, the new approach is an unqualiÿed success, removing all rejected vertices and producing output meshes of high quality; mesh quality degrades only when most vertices lie on the boundary. Three-dimensional isotropic meshes are also coarsened successfully, provided that there is no di culty distinguishing corners in the geometry from coarselyresolved curved surfaces; sophisticated discrete computational geometry techniques appear necessary to make that distinction. Three-dimensional anisotropic cases are still problematic because of tight constraints on legal mesh connectivity. More work is required to either improve edge contraction choices or to develop an alternative strategy for mesh coarsening for three-dimensional anisotropic meshes.

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“…The classical approach is purely combinatorial, i.e., it does not take any property of the embedding into account. This can lead to deteriorating aspect ratios as pointed out by Miller et al [51]. To enable control over the quality of the coarser triangulation we prioritize half-edge contractions based on edge length (effectively removing the shortest edges first) to favor uniform triangle sizes at a given level of the hierarchy.…”

Section: 2mentioning

confidence: 99%

Multilevel Solvers for Unstructured Surface Meshes

Aksoylu

Khodakovsky

Schröder

2005

SIAM J. Sci. Comput.

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Abstract. Parameterization of unstructured surface meshes is of fundamental importance in many applications of Digital Geometry Processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner.

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Optimal Coarsening of Unstructured Meshes

Cited by 32 publications

References 11 publications

Robust generation of high‐quality unstructured meshes on realistic biomedical geometry

Robust generation of high‐quality unstructured meshes on realistic biomedical geometry

Coarsening unstructured meshes by edge contraction

Multilevel Solvers for Unstructured Surface Meshes

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