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.

1.
Wawrzynek
,
P. A.
, and
Ingraffea
,
A. R.
, 1987, “
Interactive Finite Element Analysis of Fracture Processes: An Integrated Approach
,”
Theor. Appl. Fract. Mech.
0167-8442,
8
, pp.
137
150
.
2.
Martha
,
L. F.
,
Wawrzynek
,
P. A.
, and
Ingraffea
,
A. R.
, 1993, “
Arbitrary Crack Representation using Solid Modeling
,”
Eng. Comput.
0177-0667,
9
, pp.
63
82
.
3.
Beall
,
M. W.
, and
Shephard
,
M. S
,. 1997, “
A General Topology-Based Mesh Data Structure
,”
Int. J. Numer. Methods Eng.
0029-5981,
40
, pp.
1573
1596
.
4.
Garimella
,
R. V.
, 2002, “
Mesh Data Structure Selection for Mesh Generation and FEA Applications
,”
Int. J. Numer. Methods Eng.
0029-5981,
55
, pp.
451
478
.
5.
Remacle
,
J.-F.
,
Karamete
,
B. K.
, and
Shephard
,
M. S.
, 2000, “
Algorithm Oriented Mesh Database
,”
Proceedings of 9th International Meshing Roundtable
,
Sandia National Laboratories
, pp.
349
359
.
6.
Remacle
,
J.-F.
, and
Shephard
,
M. S.
, 2003, “
An Algorithm Oriented Mesh Database
,”
Int. J. Numer. Methods Eng.
0029-5981,
58
, pp.
349
374
.
7.
Tautges
,
T.
,
Ernst
,
C.
,
Merkley
,
K.
,
Meyers
,
R.
, and
Stimpson
,
C.
, 2004, “
MOAB, A Mesh-Oriented Database
,” Sandia National Laboratories Report SAND2004-1592, Sandia National Laboratories, Albuquerque, New Mexico (http://cubit.sandia.gov/MOABhttp://cubit.sandia.gov/MOAB).
8.
Celes
,
W.
,
Paulino
,
G. H.
, and
Espinha
,
R.
, 2005, “
A Compact Adjacency-Based Topological Data Structure for Finite Element Mesh Representation
,”
International Journal for Numerical Methods in Engineering
(in press).
9.
Löhner
,
R.
, 1988, “
Some Useful Data Structures for the Generation of Unstructured Grids
,”
Commun. Appl. Numer. Methods
0748-8025,
4
, pp.
123
135
.
10.
Owen
,
S. J.
, and
Shephard
,
M. S.
, 2003, “
Editorial: Special Issue on Trends in Unstructured Mesh Generation
,”
Int. J. Numer. Methods Eng.
0029-5981,
58
, pp.
159
160
.
11.
Paulino
,
G. H.
,
Menezes
,
I. F. M.
,
Neto
J. B. C.
, and
Martha
,
L. F. R. C.
, 1999, “
A Methodology for Self-Adaptive Finite Element Analysis—Towards an Integrated Computational Environment
,”
Comput. Mech.
0178-7675,
23
(
5-6
), pp.
361
388
.
12.
Carey
,
G. F.
,
Sharma
,
M.
, and
Wang
,
K. C.
, 1988, “
A Class of Data Structures for 2-D and 3-D Adaptive Mesh Refinement
,”
Int. J. Numer. Methods Eng.
0029-5981,
26
, pp.
2607
2622
.
13.
Hawken
,
D. M.
,
Townsend
,
P.
, and
Webster
,
M. F.
, 1992, “
The Use of Dynamic Data Structures in Finite Element Applications
,”
Int. J. Numer. Methods Eng.
0029-5981,
33
(
9
), pp.
1795
1811
.
14.
Pandolfi
,
A.
, and
Ortiz
,
M.
, 1998, “
Solid Modeling Aspects of Three-Dimensional Fragmentation
,”
Eng. Comput.
0177-0667,
14
, pp.
287
308
.
15.
Pandolfi
,
A.
, and
Ortiz
,
M.
, 2002, “
An Efficient Adaptive Procedure for Three-Dimensional Fragmentation Simulations
,”
Eng. Comput.
0177-0667,
18
, pp.
148
159
.
16.
Frey
,
P. J.
, 2000, “
About Surface Remeshing
,” in
Proceedings of the 9th International Meshing Roundtable
, pp.
123
136
.
17.
Vorsatz
,
J.
,
Rössl
,
C.
, and
Seidel
,
H.-P.
, 2003, “
Dynamic Remeshing and Applications
,”
J. Comput. Inf. Sci. Eng.
1530-9827,
3
, pp.
338
344
.
18.
Glimm
,
J.
, 2001, “
The Terascale Simulation Tools and Technology (TSTT) Center
,” http://www.tstt-scidac.orghttp://www.tstt-scidac.org, Executive Summary, 2001.
19.
Baumgart
,
B.
, 1972, “
Winged-Edge Polyhedron Representation
,” Technical Report CS-320 Stanford Artificial Intelligent Laboratory,
Stanford University
.
20.
Mäntylä
,
M.
, 1988,
An Introduction to Solid Modeling
,
Computer Science Press
, Rockville, MD.
21.
Weiler
,
K.
, 1986, “
Topological Structures for Geometric Modeling
,” Ph.D. thesis, Rensselaer Polytechnic Institute, New York.
22.
Chen
,
J.
, and
Akleman
,
E.
, 2000, “
Topologically Robust Mesh Modeling: Concepts, Data Structures, and Operations
,”
Int. J. Shape Model.
0218-6543,
5
(
2
), pp.
149
177
.
23.
Weiler
,
K.
, 1988, “
The Radial Edge Structure: A Topological Representation for Non-Manifold Geometric Boundary Modeling
,”
Geometric Modeling for CAD Applications
,
J. L.
Encarnação
,
H. W.
McLaughlin
, ed.,
Elsevier Science Publishers
, Amsterdam, pp.
3
36
.
24.
Lee
,
S. H.
, and
Lee
,
K.
, 2001, “
Partial Entity Structure: A Compact Non-Manifold Boundary Representation Based on Partial Topological Entities
,”
Proceedings of the sixth ACM Symposium on Solid Modeling and Applications
, pp.
159
170
.
25.
Lee
,
S. H.
, and
Lee
,
K.
, 2001, “
Partial Entity Structure: A Compact Boundary Representation for Non-Manifold Geometric Modeling
,”
J. Comput. Inf. Sci. Eng.
1530-9827,
1
(
4
), pp.
356
365
.
26.
Campagna
,
S.
,
Kobbelt
,
L.
, and
Seidel
,
H.-P.
, 1999, “
Directed Edges—A Scalable Representation for Triangle Meshes
,”
Journal of Graphics Tools
,
4
(
3
), pp.
1
12
.
27.
Rossignac
,
J.
, 1999, “
Edgebreaker: Connectivity Compression for Triangle Meshes
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
5
(
1
), pp.
47
61
.
28.
Cignoni
,
P.
,
De Floriani
,
L.
,
Magillo
,
P.
,
Puppo
,
E.
, and
Scopigno
,
R.
, 2003, “
Selective Refinement Queries for Volume Visualization of Unstructured Tetrahedral Meshes
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
10
(
1
),
29
45
.
29.
De Floriani
,
L.
, and
Hui
,
A.
, 2003, “
A Scalable Data Structure for Three-Dimensional Non-Manifold Objects
,”
Eurographics Symposium on Geometry Processing
, pp.
72
82
.
30.
Cignoni
,
P.
,
Montani
,
C.
,
Puppo
,
E.
, and
Scopigno
,
R.
, 1997, “
Multiresolution Representation and Visualization of Volume Data
,”
IEEE Trans. Vis. Comput. Graph.
1077-2626,
3
(
4
), pp.
352
369
.
31.
Kobbelt
,
L.
,
Bareuther
,
T.
, and
Seidel
,
H.-P.
, 2000, “
Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity
,”
Proceedings of Eurographics ‘00
, pp.
249
260
.
32.
De Floriani
,
L.
,
Magillo
,
P.
,
Puppo
,
E.
, and
Sobrero
,
D.
, 2002, “
A Multi-Resolution Topological Representation for Non-Manifold Meshes
,”
Proceedings of Solid Modeling’02
, pp.
17
21
.
33.
Silva
,
F. G. M.
, and
Gomes
,
A. J. P.
, 2003, “
Adjacency And Incidence Framework—A Data Structure for Efficient and Fast Management of Multiresolution Meshes
,”
Proceedings of the 1st International Conference on Computer Graphics and Interactive Techniques
, Melbourne, Australia, pp.
159
166
.
34.
Wang
,
H.
, and
Li
,
J.
, 2000, “
OctMesh—Interactive Mesh Browsing over the Internet
,”
International Conference on Information Technology: Coding and Computing (ITCC’00)
, pp.
104
108
.
35.
Rossignac
,
J.
, 2001, “
3D Compression Made Simple: Edgebreaker with Zip&Wrap on a Corner-Table
,”
IEEE International Conference on Shape Modeling and Applications
, pp.
278
283
.
36.
Sutradhar
,
A.
, and
Paulino
,
G. H.
, 2004, “
A Simple Boundary Element Method for Problems of Potential in Non-Homogeneous Media
,”
Int. J. Numer. Methods Eng.
0029-5981,
60
(
13
), pp.
2203
2230
.
37.
Tautges
,
T. J.
, 2004, “
MOAB-SD: Integrated Structured and Unstructured Mesh Representation
,”
Eng. Comput.
0177-0667,
20
, pp.
286
293
.
38.
Stroustrup
,
B.
, 1997,
The C++ Programming Language
,
Addison-Wesley
, Reading, MA.
39.
Luebke
,
D.
,
Reddy
,
M.
,
Cohen
,
J. D.
,
Varshney
,
A.
,
Watson
,
B.
, and
Huebner
,
R.
, 2003,
Level of Detail for 3D Graphics
,
Morgan Kaufmann Publisher
, Elsevier Science, San Francisco, CA.
40.
Alliez
,
P.
,
Meyer
,
M.
, and
Desbrun
,
M.
, 2002, “
Interactive Geometry Remeshing
,”
ACM Trans. Graphics
0730-0301,
21
(
3
), pp.
347
354
.
41.
Cormen
,
T. H.
,
Leiserson
,
C. E.
,
Rivest
,
R. L.
, and
Stein
,
C.
, 2001,
Introduction to Algorithms
,
2nd ed.
,
The MIT Press
, Cambridge, MA.
42.
Bulka
,
D.
, and
Mayhew
,
D.
, 2000,
Efficient C++—Performance Programming Techniques
,
Addison-Wesley
, Reading, MA.
43.
Knuth
,
D. E.
, 1997,
The Art of Computer Programming
,
3rd Edition
,
Addison-Wesley
; Reading, MA, Vol.
1
.
44.
Latta
,
L.
, 2004, “
Building a Million Particle System
,”
Game Developers Conference
, March 22–24, San Jose, California.
45.
Velho
,
L.
, and
Gomes
,
J.
, 2000, “
Variable Resolution 4-K Meshes: Concepts and Applications
,”
Comput. Graph. Forum
1067-7055,
19
(
4
), pp.
195
214
.
46.
Walters
,
M. C.
,
Paulino
,
G. H.
, and
Dodds
,
R. H.
, 2004, “
Stress Intensity Factors for Surface Cracks in Functionally Graded Materials Under Mode-I Thermomechanical Loading
,”
Int. J. Solids Struct.
0020-7683,
41
(
3-4
), pp.
1081
1118
.
47.
Namazifard
,
A.
, and
Parsons
,
I. D.
, 2004, “
A Distributed Memory Parallel Implementation of The Multigrid Method for Solving Three-Dimensional Implicit Solid Mechanics Problems
,”
Int. J. Numer. Methods Eng.
0029-5981,
61
, pp.
1173
1208
.
You do not currently have access to this content.