Abstract
This work presents a new approach to conformal all-quadrilateral mesh adaptation. Most current quadrilateral adaptivity techniques rely on mesh refinement or a complete remesh of the domain. In contrast, we introduce a new method that incorporates both conformal refinement and coarsening strategies on an existing mesh of any density or configuration. Given a sizing function, this method modifies the mesh by combining template-based quadrilateral refinement methods with recent developments in localized quadrilateral coarsening and quality improvement into an automated mesh adaptation routine. Implementation details and examples are included.
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References
Parrish, M., Borden, M., Staten, M.L., Benzley, S.E.: A Selective Approach to Conformal Refinement of Unstructured Hexahedral Finite Element Meshes. In: Proceedings of 16th International Meshing Roundtable, pp. 251–268 (2007)
Dewey, M.W.: Automated Quadrilateral Coarsening by Ring Collapse, Master’s Thesis, Brigham Young University, Provo (2008)
Anderson, B.D., Shepherd, J.F., Daniels, J., Benzley, S.E.: Quadrilateral Mesh Improvement, Research Note. In: 17th International Meshing Roundtable (2008)
Blacker, T.D., Stephenson, M.B.: Paving: A New Approach to Automated Quadrilateral Mesh Generation. International Journal for Numerical Methods in Engineering 32(4), 811–847 (1991)
Quadros, W.R., Vyas, V., Brewer, M., Owen, S.J., Shimada, K.: A Computational Framework for Generating Sizing Function in Assembly Meshing. In: Proceedings of 14th International Meshing Roundtable, pp. 55–72 (2005)
Borouchaki, H., Frey, P.J.: Optimization Tools for Adaptive Surface Meshing, AMD Trends in Unstructured Mesh Generation. ASME 220, 81–88 (1997)
Borouchaki, H., Frey, P.J.: Adaptive Triangular Quadrilateral Mesh Generation. International Journal for Numerical Methods in Engineering 41, 915–934 (1998)
Feng, Y.T., Peric, D.: Coarse Mesh Evolution Strategies in the Galerkin Multigrid Method with Adaptive Remeshing for Geometrically Non-linear Problems. International Journal for Numerical Methods in Engineering 49, 547–571 (2000)
Botkin, M.E., Wang, H.P.: An Adaptive Mesh Refinement of Quadrilateral Finite Element Meshes Based upon an a posteriori Error Estimation of Quantities of Interest: Modal Response. Engineering with Computers 20, 38–44 (2004)
Baehmann, P.L., Shephard, M.S.: Adaptive Multiple-Level h-Refinement in Automated Finite Element Analyses. Engineering with Computers 5, 235–247 (1989)
Branets, L., Carey, G.F.: Smoothing and Adaptive Redistribution for Grids with Irregular Valence and Hanging Nodes. In: Proceedings of 13th International Meshing Roundtable, pp. 333–344 (2004)
Zhang, Y., Bajaj, C.: Adaptive and Quality Quadrilateral/Hexahedral Meshing From Volumetric Data. In: Proceedings of 13th International Meshing Roundtable, pp. 365–376 (2004)
Jiao, X., Colombi, A., Ni, X., Hart, J.C.: Anisotropic Mesh Adaptation for Evolving Triangulated Surfaces. In: Proceedings of 15th International Meshing Roundtable, pp. 173–190 (2006)
Sandhu, J.S., Menandro, F.C.M., Liebowitz, H.: Hierarchical Mesh Adaptation of 2D Quadrilateral Elements. Engineering Fracture Mechanics 50, 727–735 (1995)
Albuquerque, N.M.: Cubit 11.1 user documentation, Sandia National Laboratories (2009), http://cubit.sandia.gov/documentation.html
Borouchaki, H., Hecht, F., Frey, P.J.: Mesh Gradation Control. International Journal for Numerical Methods in Engineering 13, 1143–1165 (1998)
Persson, P.-O.: Mesh Size Functions for Implicit Geometries and PDE-based Gradient Limiting. Engineering with Computers 22(2), 95–109 (2006)
Schneiders, R.: Refining Quadrilateral and Hexahedral Element Meshes. Numerical Grid Generation in Computational Field Simulations 1, 679–688 (1996)
Staten, M.L., Benzley, S.E., Scott, M.: A Methodology for Quadrilateral Finite Element Mesh Coarsening. Engineering with Computers 24, 241–251 (2008)
Kinney, P.: Cleanup: Improving Quadrilateral Finite Element Meshes. In: Proceedings of 6th International Meshing Roundtable, pp. 449–461 (1997)
CUBIT 11.1 Geometry and Mesh Generation Toolkit, Sandia National Laboratories (2009), http://cubit.sandia.gov
Anderson, B.D.: Automated All Quadrilateral Mesh Adaptation through Refinement and Coarsening, Master’s Thesis, Brigham Young University, Provo (2009)
ADINA-AUI 8.5.2, ADINA R & D Inc. (2008), http://www.adina.com
Hansen, G., Zardecki, A.: Unstructured Surface Mesh Adaptation Using the Laplace-Beltrami Target Metric Approach. Journal of Computational Physics 225, 165–182 (2007)
Harris, N.: Conformal Refinement of All-Hexahedral Finite Element Meshes, Master’s Thesis, Brigham Young University, Provo (2004)
Woodbury, A.: Localized Coarsening of Conforming All-Hexahedral Meshes, Master’s Thesis, Brigham Young University, Provo (2008)
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Anderson, B.D., Benzley, S.E., Owen, S.J. (2009). Automatic All Quadrilateral Mesh Adaption through Refinement and Coarsening. In: Clark, B.W. (eds) Proceedings of the 18th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04319-2_32
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DOI: https://doi.org/10.1007/978-3-642-04319-2_32
Publisher Name: Springer, Berlin, Heidelberg
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