Efficient Handling of Implicit Entities in Reduced Mesh Representations

[+] Author and Article Information
Waldemar Celes, Rodrigo Espinha

Tecgraf/PUC-Rio, Computer Science Department,  Pontifical Catholic University of Rio de Janeiro, Rua Marquês de São Vicente 225, Rio de Janeiro, RJ, 22450-900, Brazil

Glaucio H. Paulino1

Department of Civil and Environmental Engineering, University of Illinois at Urbana–Champaign Newmark Laboratory, MC-250, 205 North Mathews Avenue, Urbana, IL 61801-2397paulino@uiuc.edu

Two elements are considered adjacent if they share the same facet.


To whom correspondence should be addressed.

J. Comput. Inf. Sci. Eng 5(4), 348-359 (Aug 01, 2005) (12 pages) doi:10.1115/1.2052830 History: Received October 11, 2004; Revised August 01, 2005

State-of-the-art numerical analyses require mesh representation with a data structure that provides topological information. Due to the increasing size of the meshes currently used for simulating complex behaviors with finite elements or boundary elements (e.g., adaptive and/or coupled analyses), several researchers have proposed the use of reduced mesh representations. In a reduced representation, only a few types of the defined topological entities are explicitly represented; all the others are implicit and retrieved “on-the-fly,” as required. Despite being very effective in reducing the memory space needed to represent large models, reduced representations face the challenge of ensuring the consistency of all implicit entities when the mesh undergoes modifications. As implicit entities are usually described by references to explicit ones, modifying the mesh may change the way implicit entities (which are not directly modified) are represented, e.g., the referenced explicit entities may no longer exist. We propose a new and effective strategy to treat implicit entities in reduced representations, which is capable of handling transient nonmanifold configurations. Our strategy allows, from the application point of view, explicit and implicit entities to be interchangeably handled in a uniform and transparent way. As a result, the application can list, access, attach properties to, and hold references to implicit entities, and the underlying data structure ensures that all such information remains valid even if the mesh is modified. The validity of the proposed approach is demonstrated by running a set of computational experiments on different models subjected to dynamic remeshing operations.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Effect of an edge collapse operator on implicit entities: (a) the original model, (b) the modified model (see Ref. 3). The edge {2,6} is collapsed with vertex 6 replacing vertex 2; edge e {2,4} and face f {1,2,4} are changed to edge e′ {4,6} and face f′ {1,4,6}, respectively. Each arrow indicates the selected entity orientation.

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Figure 2

Topological entities defined by the data structure: solid boxes indicate explicit entities and dashed boxes indicate implicit entities. The arrows illustrate access provided by the topological attributes stored at the entities. From an element, we have access to its node incidence, to its adjacent elements, and to the anchored facets, edges, and vertices; from a node, we have access to one of its incident elements; from a facet-use, edge-use, and vertex-use, we have access to the anchoring element; finally, from a facet, edge, and vertex, we have access to the corresponding entity-use associated to the anchoring element. Besides these direct topological accesses, the data structure makes use of element templates to extract topological relationships among the entity-uses associated to each element.

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Figure 3

The 4-byte word layout to identify elements and implicit entities. The first 4 bits are only used for implicit entities.

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Figure 4

An edge collapse operator based on node and element removals and insertions: (a) original model; (b) all elements incident to a vertex are removed; (c) the isolated corresponding node is removed; (d) all removed elements, which were not adjacent to the collapsing edge, are reinserted with new connectivity

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Figure 5

Nonmanifold configuration after element removal

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Figure 6

Two distinct edges of a 2D mesh, sharing the same bounding nodes, may result in different configurations: (a) a manifold-configuration and (b) a nonmanifold configuration

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Figure 7

Two distinguished edges of a 2D mesh sharing the same bounding nodes may result in different configurations: (a) a manifold-configuration and (b) a nonmanifold configuration

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Figure 8

An example of how implicit entities are managed, based on an edge shared by four different elements of a 3D model: (a) 3D schematic view of a cutting plane (π plane) crossing an edge shared by hexahedral elements; (b) the resulting cross-section of the edge and its 4 incident elements, with element E1 being the anchor of the edge (⤈ denotes the anchor sign); (c) element E1 is removed, thus adding new entries in the mapping and reverse mapping tables; (d) element E2 is removed, and no mapping related to the edge is needed because it is not the anchor; (e) element E4 is removed, adding new entries to the tables

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Figure 9

Plot of time (seconds) vs number of elements for model construction from scratch. The data were extracted from Table 1. The data points associated to the 64×64×64 models are outside the plotting window.

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Figure 10

A 4-k variable resolution mesh covering a square domain: (a) original 4-element mesh topology; (b) model topology after splitting the bottom edge once; (c) model topology after splitting the bottom edge a second time

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Figure 11

A simple example illustrating the support for mesh refinement along the circular edge. From left to right, and top to bottom: geometric model; initial mesh configuration; and four different meshes achieved by iteratively splitting the boundary edges and by applying a filter to accommodate the internal nodes.

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Figure 12

Models used on the numerical tests: top, surface crack model with quadratic hexahedral and pentahedral mesh; bottom, Titan IV solid model with linear hexahedral mesh

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Figure 13

Model configurations after removing half of the elements in random order: top, surface crack model; bottom, Titan IV solid model

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Figure 14

Model configurations after reconstructing the model without recovering the original boundary attributes: top, surface crack model; bottom, Titan IV solid model



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