Efficient Adaptive Meshing of Parametric Models

[+] Author and Article Information
Alla Sheffer

Computer Science Department, Technion, Haifa, Israel, 32000

Alper Üngör

Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 61801

J. Comput. Inf. Sci. Eng 1(4), 366-375 (Oct 01, 2001) (10 pages) doi:10.1115/1.1429640 History: Received August 01, 2001; Revised October 01, 2001
Copyright © 2001 by ASME
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Light,  R., and Gossard,  D., 1982, “Modification of Geometric Models Through Variational Geometry,” CAD, 14, No. 4, pp. 209–214.
Roller, D., 1991, “Advances Methods for Parametric Design,” Geometric Modeling Methods and Applications, pp. 251–266.
Raghothama, S., and Shapiro, V., 1999, “Consistent Updates in Dual Representation Systems,” Solid Modeling’99, pp. 65–75.
Chung, J. C. H., Hwang, T-S., Wu, C-T., Jiang, Y., Wang, J-Y., Bai, Y., and Zou, H., 1999, “Extended Variational Design Technology-Foundation for Integrated Design Automation,” Solid Modeling’99, pp. 13–22.
Parametric Technology Corporation, Pro/ENGINEER, http://www.ptc.com
SDRC, Ideas, http://www.sdrc.com
Unigraphics Solutions, UG/Solid-Modeling, http://www.ugsolutions.com
Halpern, M., 1997, “Industrial Requirements and Practices in Finite Element Meshing: A Survey of Trends,” 6th International Meshing Roundtable, pp. 399–411.
Owen, S. J., 1998, “A Survey of Unstructured Mesh Generation Technology,” 7th International Meshing Roundtable, pp. 239–267.
Sheffer, A., Blacker, T. D., and Bercovier, M., 1998, “Towards the Solution of Fundamental Issues in Cad-Fem Integration,” Proc. 4th World Congress on Computational Mechanics.
CAD/FE Integration Working Group, NAFEMS Finite Element Methods & Standards, 1996, How to—Integrate CAD and Analysis.
Blacker, T., 2000, “Meeting the Challenge for Automated Conformal Hexahedral Meshing,” 9th International Meshing Roundtable, pages 11–20.
Sheffer,  A., Blacker,  T. D., and Bercovier,  M., 2000, “Virtual Topology Operators for Meshing,” International Journal of Computational Geometry and Applications, 10, No. 2.
Butlin, G., and Stops, C., 1996, “Cad Data Repair,” 5th International Meshing Roundtable, pp. 7–12.
Steinbrenner, J. P., Wyman, N. J., and Chawner, J. R., 2000, “Fast Surface Meshing on Imperfect Cad Models,” 9th International Meshing Roundtable, pp. 33–42.
Capoyleas,  V., Chen,  X., and Hoffman,  C. M., 1996, “Generic Naming in Generative, Constraint-Based Design,” Computer Aided Design (CAD), 28, No. 1, pp. 17–26.
Fluent Inc. GAMBIT CFD Pre-Processor. http://www.fluent.com/software/gambit/index.htm
Staten, M. L., Canann, S. A., and Owen, S. J., 1998, “Bmsweep: Locating Interior Nodes During Sweeping,” 7th International Meshing Roundtable, pp. 7–18.
Knupp,  P. M., 1999, “Applications of Mesh Smoothing: Copy, Morph, and Sweep on Unstructured Quadrilateral Meshes,” Int. J. Numer. Methods Eng., 45, 37–45.
Edelsbrunner, H., 2000, “Triangulations and Meshes in Computational Geometry,” Acta Numerica, pp. 133–213.
Teng,  Shang-Hua, and Wai Wong,  Chi, 2000, “Unstructured Mesh Generation: Theory, Practice, and Perspectives,” Int. J. Computational Geometry & Applications, 10, No. 3, pp. 227–266.
Calvo, N. A., and Idelsohn, S. R., 1999, “All-Hexahedral Mesh Smoothing with a Normalized Jacobian Metric Combining Gradient Driven and Simulated Annealing,” MECOM 99, Sexto Congreso Argentino de Mecanica Computacional. Mendoza-Argentina.
Knupp, P. M., 2000, “Hexahedral Mesh Untangling and Algebraic Mesh Quality Metrics,” 9th International Meshing Roundtable, pp. 173–183.
Knupp, P. M., 1998, “Winslow Smoothing on Two-Dimensional Unstructured Meshes,” 7th International Meshing Roundtable, pp. 449–458.
Freitag, L. A., and Knupp, P. M., 1999, “Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number,” 8th International Meshing Roundtable, pp. 247–258.
Ruppert, J., 1993, “A New and Simple Algorithm for Quality 2-Dimensional Mesh Generation,” In Proc. 4th ACM-SIAM Symp. on Disc. Algorithms, pp. 83–92.
Shewchuk, J. R., 1998, “Tetrahedral Mesh Generation by Delaunay Refinement,” In 14th Annual ACM Symposium on Computational Geometry, pp. 86–95.
Cheng, S.-W., Dey, T. K., Edelsbrunner, H., Facello, M. A., and Teng, S.-T., 1999, “Sliver Exudation,” In Proc. 15th ACM Symp. Comp. Geometry.
Edelsbrunner, H., Li, X.-Y., Miller, G., Stathopoulos, A., Talmor, D., Teng, S.-H., Üngör, A., and Walkington, N., 2000, “Smoothing and Cleaning up Slivers,” In Proc. 32nd ACM Symp. on Theory of Computing.
Edelsbrunner, H., and Guoy. D., 2001, “Sink-insertion for Mesh Improvement,” Proc. 17th ACM Symp. on Computational Geometry.
Rivara,  M.-C., 1997, “New Longest-Edge Algorithms for the Refinement and/or Improvement of Unstructured Triangulations,” Int. J. Numer. Methods Eng., 40, pp. 3313–3324.
Li,  X. Y., Teng,  S.H., and Üngör,  A., 1999, “Simultaneous Refinement and Coarsening Adaptive Meshing with Moving Boundaries,” Eng. Comput., 15, 292–302.
Li,  X. Y., Teng,  S. H., and Üngör,  A., 2000, “Biting: Advancing Front Meets Sphere Packing,” Int. J. Numer. Methods Eng., 49, 61–81.
Miller,  G. L., Talmor,  D., and Teng,  S.-H., 1999, “Optimal Coarsening of Unstructured Meshes,” Journal of Algorithms, 31, 29–65.
Shimada, K., and Gossard, D. C., 1995, “Bubble Mesh: Automated Triangular Meshing of Non-Manifold Geometry by Sphere-Packing,” ACM Symposium on Solid Modeling Foundations and Applications, pp. 409–419.
Hoppe, H., 1996, “Progressive Meshes,” SIGGRAPH96, pp. 99–108.
Garland, M., and Heckbert, P. S., 1997, “Surface Simplification Using Quadric Error Metrics,” Proc. SIGGRAPH’97, pp. 209–221.
Schneiders, R., 1995, “Automatic Generation of Hexahedral Finite Element Meshes,” 4th International Meshing Roundtable, pp. 103–114.
Hassan, O, Sorenson, K., Morgan, K., and Weatherill, N. P., 2000, “An Adaptive Unstructured Mesh Method for Transient Flows Involving Moving Boundaries,” Proc. 7th International Conference on Numerical Grid Generation in Computational Field Simulations.
Sandia National Laboratories. Cubit Mesh Generation Toolkit. http://endo.sandia.gov/cubit
Blacker, T. D., 1996, “The Cooper Tool,” 5th International Meshing Roundtable, pp. 13–29.
Mitchell, S., and Tautges, T. J., 1995, “Pillowing Doublets: Refining a Mesh to Ensure that Faces Share at Most One Edge,” 4th Internatinal Meshing Roundtable, pp. 231–240.
Schneiders, R., 1996, “Refining Quadrilateral and Hexahedral Element Meshes,” 5th International Conference on Numerical Grid Generation in Computational Field Simulations, pp. 679–688.
Tautges,  T. J., Blacker,  T. D., and Mitchell,  S. A., 1996, “The Whiskerweaving Algorithm: A Connectivity-Based Method for Constructingall-Hexahedral Finite Element Meshes,” Int. J. Numer. Methods Eng., 39, No. 19, pp. 3327–3349.


Grahic Jump Location
Meshing an “L” shaped model. (a) Original design model. (b) Mesh model (after simplification). (c) Hexahedral mesh.
Grahic Jump Location
Adjusting the mesh of “L” shape in Fig. 1 to different parameter sizes. (a) Design model. (b) Mesh Model (same topology as original mesh model). (c) Reassigned Mesh. (d) Mesh after connectivity adjustment (whisker-sheet splitting, 5.2.2).
Grahic Jump Location
A pump housing model. (a) Design model. (b) Mesh model (after simplification). (c) A tetrahedral mesh of the model.
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Feature size impact on mesh generation. A notch narrower than prescribed element size (a), has little impact on analysis, and hence can be suppressed in the mesh model (b). When the notch width increases above the mesh size (c), it starts to have an impact on analysis results. Hence, the model needs a mesh reflecting it (d).
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Copy of interior face nodes using a background mesh. (a) Mesh of the original face. (b) New, modified face with copied boundary nodes. (c) Background mesh of (a). (d) Background mesh and copied interior node on (b).
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Adjusting the mesh for a simple bracket. The changed parameters include: hole radii, blends radius, and base width. The changes are relatively small, hence mesh copy with smoothing is sufficient to get a good quality mesh. (a) Original model. (b) New model.
Grahic Jump Location
Adaptive re-meshing of a 2D graded mesh using the refinement technique. (a) Original mesh with 169 nodes. (b) The model is stretched by a factor of 2 along X direction. This creates 54 bad elements in the mesh. (c) Final mesh is a result of 75 circumcenter points insertions.
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Surface mesh of a dodecahedron. (a) Original mesh with 290 nodes. (b) The model is stretched by a factor of 2 along X direction (for illustration purposes the top view is chosen). The stretching creates 98 bad simplices. (c) Inserting 43 circumcenter points removes all the bad simplices.
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Maintaining a sphere packing (a) Original mesh generated by a sphere packing. (b) Packing is no longer good as big gaps in the domain are introduced. (c) Packing is modified to be a good packing. (d) Delaunay Triangulation of the points in the packing gives a good quality mesh.
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Refinement algorithm may create over-refined meshes. (a) Original mesh. (b) Refinement based method computes mesh of the same model shrunk in Y direction by a factor of 1/2.
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Adjusting the mesh for a model composed of two sweepable parts. The parameter that changes is the tube height (from 2 to 5). Applying only copy and smoothing will generate highly stretched elements on the pipe. (a) Original model. (b) Mesh after copy. (c) Mesh after re-meshing the pipe part.
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(a) Four whisker sheets (a-d) in a two element hexahedral mesh. (b) Two whisker sheets in a cylinder mesh (highlighted).
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A whisker sheet S with Z pointing in the direction of the sheet axis.
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Whisker sheet removal and split. (a) Initial model. (b) Model after a sheet removal. (c) Model after a sheet split.
Grahic Jump Location
Adapting a hexahedral mesh using the whisker sheet removal operation. (a) Mesh of the original model. (b) Copied mesh of the new model (cylinder radius of 5, replaced by two radii of 7 and 3). (c) Mesh after single sheet removal. (d) Mesh after smoothing. (e) Final mesh after one more sequence of sheet removal and smoothing.
Grahic Jump Location
Volume mesh of part of a booster rocket containing the solid propellant and the star shaped cavity inside it. The fins of the star are about two elements thick. (a) Original mesh with 36726 tetrahedra. (b) Stretching the model along X and Z directions makes about 3% of the tetrahedra bad. (c) Inserting 2170 circumcenters removes all of the bad simplices.
Grahic Jump Location
Meshing a crank-shaft model after parameter modification. (a) Original design model. (b) Mesh model, after suppression of blends and subdivision into 5 sub-volumes. (c) Mesh of the original model. (d) New design model. (e) New mesh model with mesh mapped from (c). (f) Final mesh of the new model. The mesh adjustment included removal of a mesh sheet in the central board and several sheet splits in the right cylindrical tip.



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