Reliability of automatic 3D mesh generation

Abstract. A simple local bisection refinement algorithm for the adaptive refinement of n-simplicial grids is presented. The algorithm requires that the vertices of each simplex be ordered in a special way relative to those in neighboring simplices. It is proven that certain regular simplicial grids on [0, 1]n have this property, and the more general grids to which this method is applicable are discussed. The edges to be bisected are determined by an ordering of the simplex vertices, without local or global computation or communication. Further, the number of congruency classes in a locally refined grid turns out to be bounded above by n, independent of the level of refinement.

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“…instance Shephard and Georges [28] or Bern and Eppstein 10]. Mesh refinement techniques will be discussed below.…”

mentioning

confidence: 99%

Local Bisection Refinement for N-Simplicial Grids Generated by Reflection

Maubach¹

1995

SIAM J. Sci. Comput.

262

197

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“…It implements the Radial Edge structure [12] to provide the topological adjacencies between vertex, edge, face and region elements in the geometric model. By using the model abstractions all components of the simulation framework are independent of the specifics of any particular geometric modeler [10], [14], [16], [28]. Figure 5 exemplifies the interaction of the analysis tool, the discretization tools and the attribute system with the modeler system through the model abstraction.…”

Section: Model Abstraction To Link With Cadmentioning

confidence: 99%

“…For example, it has been shown how the geometric modeling system tolerance information, which is not represented in the exchange specification, is needed to support automatic mesh generation functions [10]. On the other hand, it has also been shown that robust automatic mesh generators can be developed [10], [11] that directly rely on the geometry engine of the solid modeling system through the abstraction of topology [12].…”

Section: Geometric Domainmentioning

confidence: 99%

Embedding Reliable Numerical Analysis Capabilities into an Enterprise-Wide Information System

Klaas

Shepard

2001

EWC

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A simulation environment to support engineering design embedded in an enterprise wide information system is presented. The environment consists of a set of structures and managers housing the problem definition, tools for controlling the simulation model construction and execution, and the interaction of simulation processes with the product data management system. The issues associated with the introduction of automated and adaptive geometry-based simulation processes into the engineering design process are emphasized.

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“…We refer to the association of the mesh with respect to the geometric model as classification [31,34]. In particular, the mesh topological entities are classified with respect to the geometric model topological entities upon which they lie as defined below.…”

Section: Domain Discretizationmentioning

confidence: 99%

Toward interoperable mesh, geometry and field components for PDE simulation development

Chand

Diachin

Li³

et al. 2007

Engineering with Computers

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Mesh-based PDE simulation codes are becoming increasingly sophisticated and rely on advanced meshing and discretization tools. Unfortunately, it is still difficult to interchange or interoperate tools developed by different communities to experiment with various technologies or to develop new capabilities. To address these difficulties, we have developed component interfaces designed to support the information flow of mesh-based PDE simulations. We describe this information flow and discuss typical roles and services provided by the geometry, mesh, and field components of the simulation. Based on this delineation for the roles of each component, we give a high-level description of the abstract data model and set of interfaces developed by the Department of Energy's Interoperable Tools for Advanced Petascale Simulation (ITAPS) center. These common interfaces are critical to our interoperability goal, and we give examples of several services based upon these interfaces including mesh adaptation and mesh improvement.

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Reliability of automatic 3D mesh generation

Cited by 43 publications

References 7 publications

Local Bisection Refinement for N-Simplicial Grids Generated by Reflection

Local Bisection Refinement for N-Simplicial Grids Generated by Reflection

Embedding Reliable Numerical Analysis Capabilities into an Enterprise-Wide Information System

Toward interoperable mesh, geometry and field components for PDE simulation development

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