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Smoothing Techniques

Smoothing techniques for finite element mesh generation. Nodes locations are adjusted in order to improve overall element quality without affecting element topology.

MESHING
RESEARCH
CORNER

Balendran, Bala

    "A Direct Smoothing Method For Surface Meshes", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.189-193, October 1999
    keywords:
    • mesh smoothing
    • direct method
    • surface mesh
    • quadrilateral
    • triangular
    Abstract
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Benitez, Domingo, Eduardo Rodriguez, Jose Maria Escobar, and Rafael Montenegro
    "Performance Evaluation of a Parallel Algorithm for Simultaneous Untangling and Smoothing of Tetrahedral Meshes", 22nd International Meshing Roundtable, Springer-Verlag, pp.579-598, October 13-16 2013
    keywords:
    • parallel
    • untangling
    • smoothing
    • tetrahedral meshes
    • performance
    Abstract
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Berndt, Markus and Mikhail Shashkov
    "Multilevel accelerated optimization for problems in grid generation", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.351-359, Sept. 2003
    keywords:
    • smoothing
    • optimization
    • multilevel methods
    • coarsening
    • untangling
    • triangle
    • anisotropy
    Abstract
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Bidmon, Katrin, Dirc Rose and Thomas Ertl
    "Intuitive, Interactive, and Robust Modification and Optimization of Finite Element Models", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.59-70, September 19-22 2004
    keywords:
    • freeform modeling
    • interaction
    • smoothing
    • optimization
    • manipulators
    Abstract
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Branets L. and G.F. Carey
    "Cell quality metric and variational grid smoothing algorithm", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.371-390, Sept. 2003
    keywords:
    • smoothing
    • quality
    • metrics
    Abstract
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Branets, Larisa and Graham F. Carey
    "Smoothing and Adaptive Redistribution for Grids With Irregular Valence and Hanging Nodes", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.333-344, September 19-22 2004
    keywords:
    • smoothing
    • adaptive redistribution
    • quality metrics
    • refinement
    • structured
    Abstract
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Brewer, Michael, Lori Freitag Diachin, Patrick Knupp, Thomas Leurent and Darryl Melander
    "The Mesquite Mesh Quality Improvement Toolkit", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.239-250, Sept. 2003
    keywords:
    • quality
    • smoothing
    • Mesquite
    • toolkit
    Abstract
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Canann, Scott A., Joseph R. Tristano, Matthew L. Staten
    "An Approach to Combined Laplacian and Optimization-Based Smoothing for Triangular, Quadrilateral, and Quad-Dominant Meshes", 7th International Meshing Roundtable, Sandia National Labs, pp.479-494, October 1998
    keywords:
    • smoothing
    • Laplacian smoothing
    • optimization-based smoothing
    • triangle
    • quadrilateral
    • metric
    Abstract
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Caplan, Philip, Robert Haimes, Dacid L. Darmofal, and Steven R. Allmaras
    "Anisotropic advancing front quadrangulationwith optimization-based smoothing", Research Notes, 22nd International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 13-16 2013
    keywords:
    • anisotropic
    • quadrangulation
    • optimization-based smoothing
    Abstract
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Cascon, J.M., R. Montenegro, J.M. Escobar, E. Rodriguez,and G. Montero
    "The Meccano Method forAutomatic Tetrahedral Mesh Generation ofComplex Genus-Zero Solids", Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.463-480, October 25-28 2009
    keywords:
    • Tetrahedral mesh generation
    • local refinement
    • nested meshes
    • meshuntangling and smoothing
    • surface and volume parametrization.
    Abstract
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Chen, Long
    "Mesh Smoothing Schemes Based on Optimal Delaunay Triangulations", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.109-120, September 19-22 2004
    keywords:
    • anisotropic mesh adaptation
    • Delaunay
    • Voronoi tessellation
    • smoothing
    Abstract
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Chen, Zhijian, Joseph R. Tristano and Wa Kwok
    "Combined Laplacian and optimization-based smoothing for quadratic mixed surface meshes", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.201-213, Sept. 2003
    keywords:
    • smoothing
    • optimization-based smoothing
    • constrained-Laplacian smoothing
    • smoothing objective function
    • surface meshing
    • smoothing quadratic elements
    Abstract
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Dhondt, Guido D.
    "Unstructured 20-Node Brick Element Meshing", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.369-376, October 1999
    keywords:
    • hexahedra
    • mesh generation
    • cutting
    • smoothing
    • quadratic
    • inside-out
    • grid-based
    Abstract
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Djidjev, Hristo N.
    "Force-Directed Methods for Smoothing Unstructured Triangular and Tetrahedral Meshes", Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.395-406, October 2000
    keywords:
    • smoothing
    • force-directed methods
    • unstructured
    • triangle
    • tetrahedra
    Abstract
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Dudley, Clifton R. and Steven J. Owen
    "Degenerate Hex Elements", 23rd International Meshing Roundtable, Elsevier Ltd., October 12-15 2014
    keywords:
    • degenerate hexahedral elements
    • grid-based
    • overlay grid
    • smoothing
    • sculpt
    Abstract
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Elbert, Gregory J., David A. Field and William H. Frey
    "When Mesh Generators Require Enhancements", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.525-537, October 1998
    keywords:
    • triangle
    • smoothing
    • quality
    • enhancements
    Abstract


Escobar, J.M., R. Montenegro, E. Rodr¥iguez, and G. Montero
    "Simultaneous Aligning and Smoothing of Surface Triangulations", Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.333-350, October 12-15 2008
    keywords:
    • Mesh alignment
    • Moving meshes
    • Mesh adaptation
    • Surface mesh smoothing
    • Node movement
    • R-adaptivity.
    Abstract
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Falsafioon, Mehdi, Sina Arabi, Francois Guibault, Ricardo Camarero
    "Smoothing of Unstructured Grids", 23rd International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-15 2014
    keywords:
    • Elliptic smoothing
    • Winslow Equation
    • Barycentric method
    • Local computational space
    • Unstructured grids
    • Mesh generation
    Abstract
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Folwell, Nate, Patrick Knupp and Michael Brewer
    "Increasing the Tau3P abort-time via mesh quality improvement", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.379-390, Sept. 2003
    keywords:
    • quality
    • smoothing
    • optimization
    • computational electromagnetics
    Abstract
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Freitag, Lori A. and Carl Ollivier-Gooch
    "A Comparison of Tetrahedral Mesh Improvement Techniques", 5th International Meshing Roundtable, Sandia National Laboratories, pp.87-106, October 1996
    keywords:
    • metric
    • optimization
    • quality
    • smoothing
    • swapping
    • topology
    Abstract
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Freitag, Lori A. and Carl Ollivier-Gooch
    "The Effect Of Mesh Quality On Solution Efficiiency", Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.249, October 1997
    keywords:
    • quality
    • smoothing
    Abstract
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Freitag, Lori A. and Patrick M. Knupp
    "Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.247-258, October 1999
    keywords:
    • improvement
    • optimization-based smoothing
    • quality
    • untangling
    • smoothing
    Abstract
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Freitag, Lori A. and Paul E. Plassmann
    "Local Optimization-Based Untangling Algorithms for Quadrilateral Meshes", Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.397-406, October 7-10 2001
    keywords:
    • quadrilateral
    • untangling
    • improvement
    • quality
    • smoothing
    Abstract
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Freitag, Lori, Mark Jones, and Paul Plassmann
    "An Efficient Parallel Algorithm for Mesh Smoothing", Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.47-58, October 1995
    keywords:
    • optimization
    • parallel processing
    • smoothing
    Abstract
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Freitag, Lori, Patrick Knupp, Todd Munson, and Suzanne Shontz
    "A Comparison Of Optimization Software For Mesh Shape-Quality Improvement Problems", Proceedings, 11th International Meshing Roundtable, Springer-Verlag, September 15-18 2002
    keywords:
    • mesh smoothing
    • optimization
    • mesh quality improvement
    • mean ratio
    Abstract
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Freitag-Diachin, Lori, Patrick Knupp, Todd Munson and Suzanne Shontz
    "A Comparison of Inexact Newton and Coordinate Descent Mesh Optimization Techniques", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.243-254, September 19-22 2004
    keywords:
    • quality
    • improvement
    • optimization
    • smoothing
    Abstract
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George, Paul Louis
    "Tet Meshing: Construction, Optimization, And Adaptation", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.133-141, October 1999
    keywords:
    • tetrahedra
    • constrained triangulation
    • Delaunay
    • overview
    • adaptivity
    • optimization
    • smoothing
    Abstract
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Herring, S. Davis, Brian Jean
    "Voronoi Meshes with Prescribed Boundaries", 24th International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-14 2015
    keywords:
    • Voronoi diagram
    • hybrid meshing
    • mesh relaxation
    Abstract
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Holder, Mike and Jim Richardson
    "Genetic Algorithms, Another Tool for Quad Mesh Optimization", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.497-504, October 1998
    keywords:
    • genetic algorithm
    • artificial intelligence
    • smoothing
    • optimization
    Abstract
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Huang, Weizhang, Lennard Kamenski,Hang Si
    "Mesh smoothing: an MMPDE moving mesh approach", 24th International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-14 2015
    keywords:
    • mesh smoothing
    • mesh optimization
    • moving mesh method
    • tetrahedral meshes
    Abstract
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Jansen, K.E and M.S. Shephard
    "On Anisotropic Mesh Generation and Quality Control in Complex Flow Problems", Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.341-349, October 7-10 2001
    keywords:
    • anisotropy
    • mesh control
    • hybrid grid generation
    • CFD
    • smoothing
    Abstract
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Jiao, Xiangmin
    "Volume and Feature Preservation in Surface Mesh Optimization", Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.359-374, September 17-20 2006
    keywords:
    • optimization
    • smoothing
    • surface meshes
    • volume conservation
    • feature detection
    Abstract
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Knupp, Patrick M.
    "Winslow Smoothing On Two-Dimensional Unstructured Meshes", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.449-457, October 1998
    keywords:
    • winslow smoothing
    • quadrilateral
    • smoothing
    • elliptic smoothing
    Abstract
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Kober, Cornelia and Matthias Muller-Hannemann
    "Hexahedral Mesh Generation for the Simulation of the Human Mandible", Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.423-434, October 2000
    keywords:
    • hexahedra
    • quadrilateral
    • optimized mesh smoothing
    • human mandible
    • cycle-elimination
    Abstract
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Leng, Juelin, Yongjie Zhang and Guoliang Xu
    "A Novel Geometric Flow-Driven Approach for Quality Improvement of Segmented Tetrahedral Meshes", 20th International Meshing Roundtable, Springer-Verlag, pp.347-363, October 23-26 2011
    keywords:
    • Segmented tetrahedral mesh
    • quality improvement
    • geometric flow-driven
    • optimization-based mesh smoothing
    • shape-preserving
    Abstract
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Lipnikov, Konstantin and Yuri Vassilevski
    "Error Estimates for Hessian-based Mesh Adaption Algorithms with Control of Adaptivity", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.345-352, September 19-22 2004
    keywords:
    • adaption
    • Hessian-based metrics
    • quality
    • error estimates
    • smoothing
    Abstract
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Lopez, J.I., M. Brovka, J.M. Escobar, J.M. Cascon, and R. Montenegro
    "T-spline Parameterization of 2D Geometries Based on the Meccano Method with a New T-mesh Optimization Algorithm", 22nd International Meshing Roundtable, Springer-Verlag, pp.57-74, October 13-16 2013
    keywords:
    • T-spline parameterization
    • simultaneous mesh untangling and smoothing
    • meccano method
    • isogeometric analysis
    • quadtree
    Abstract
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Mezentsev, Andrey A.
    "A Generalized Graph-Theoretic Mesh Optimization Model", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.255-264, September 19-22 2004
    keywords:
    • optimization
    • smoothing
    • graph-theoretic mesh model
    • algebraic multigrid
    • hybrid mesh
    Abstract
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Mukherjee, Nilanjan
    "A Hybrid, Variational 3D Smoother For Orphaned Shell Meshes", Proceedings, 11th International Meshing Roundtable, Springer-Verlag, pp.379-390, September 15-18 2002
    keywords:
    • smoothing
    • mesh
    • Laplace
    • incenter
    • concave
    • distortion
    Abstract
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Muller-Hannemann, Matthias, Cornelia Kober, Robert Sader, Hans-Florian Zeilhofer
    "Anisotropic Validation of Hexahedral Meshes for Composite Materials in Biomechanics", Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.249-260, October 7-10 2001
    keywords:
    • hexahedra
    • quality
    • optimized mesh smoothing
    • smoothning
    • human mandible
    • biomechanics
    • dual-cycle elimination method
    Abstract
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Owen, Steven J.
    "A Survey of Unstructured Mesh Generation Technology", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.239-267, October 1998
    keywords:
    • overview
    • classification
    • software
    • triangle
    • quadrilateral
    • tetrahedra
    • hexahedra
    • surface meshing
    • refinement
    • clean-up
    • smoothing
    • Delaunay
    • advancing front
    • octree
    • plastering
    • paving
    • whisker weaving
    • grid-based
    • indirect
    Abstract
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Owen, Steven J.
    "Parallel Smoothing for Grid-Based Methods", Research Notes, 21st International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 7-10 2012
    keywords:
    • grid-based
    • overlay grid
    • hexahedral mesh generation
    • parallel meshing
    • smoothing
    • optimization
    • mesh quality
    Abstract
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Paoletti, Stefano
    "A Comparison of Parametric Space vs. RealSpace Triangular Meshing Algorithms", Proceedings, 11th International Meshing Roundtable, Springer-Verlag, September 15-18 2002
    keywords:
    • mesh optimization
    • smoothing
    • interpolation tensor
    • condition number
    • polygons
    • polyhedra
    • meshless
    Abstract
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Quadros, William Roshan
    "A Case Study - Scaling Legacy Code on Next Generation Platforms", 24th International Meshing Roundtable, Elsevier Ltd., pp.Research Note, October 12-14 2015
    keywords:
    • Parallel Programming
    • MPI+X
    • Hybrid Programming Model
    • Laplace Smoothing
    • Next Generation Platforms
    Abstract
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Rand, Alexander and Noel Walkington
    "Collars and Intestines: Practical Conforming Delaunay Refinement", Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.481-497, October 25-28 2009
    keywords:
    • Tetrahedral mesh generation
    • local refinement
    • nested meshes
    • meshuntangling and smoothing
    • surface and volume parametrization.
    Abstract
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Roca, Xevi, Josep Sarrate and Antonio Huerta
    "A new least-squares approximation of affine mappings for sweep algorithms", Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.433-448, September 11-14 2005
    keywords:
    • hexahedra
    • node projection
    • smoothing
    • sweeping
    Abstract
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Ruiz-Girones, E., X. Roca, and J. Sarrate
    "Combining Size-Preserving and Smoothing Procedures for Adaptive Quadrilateral Mesh Generation", 22nd International Meshing Roundtable, Springer-Verlag, pp.19-37, October 13-16 2013
    keywords:
    • mesh size function
    • background mesh
    • adaptive process
    • quadrilateral mesh
    • gradient-limiting
    • smoothing
    Abstract
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Ruiz-Girones, Eloi and Xevi Rocab, Jose Sarrate
    "Optimizing mesh distortion by hierarchical iteration relocation of the nodes on the CAD entities", 23rd International Meshing Roundtable, Elsevier Ltd., October 12-15 2014
    keywords:
    • Mesh smoothing
    • Mesh untangling
    • Algebraic quality
    • Function optimization
    • Hierarchical approach
    Abstract
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Scott, Michael A., Matthew N. Earp, Steven E. Benzley and Michael B. Stephenson
    "Adaptive Sweeping Techniques", Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.417-432, September 11-14 2005
    keywords:
    • decomposition
    • hexahedra
    • node projection
    • smoothing
    • sweeping
    Abstract
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Shashkov, M and P. Knupp
    "Optimization-Based Reference-Matrix Rezone Strategies for Arbitrary Lagrangian-Eulerian Methods on Unstructured Meshes", Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.167-176, October 7-10 2001
    keywords:
    • ALE
    • rezoning
    • optimization
    • reference Jacobian
    • condition number
    • smoothing
    Abstract
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Shontz, Suzanne M. and Stephen A. Vavasis
    "A mesh warping algorithm based on weighted Laplacian smoothing", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.147-158, Sept. 2003
    keywords:
    • moving meshes
    • optimization-based smoothing
    • smoothing
    • tetrahedra
    • cardiology
    • bio-medical
    • faceted surface representations
    Abstract
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Sirois, Yannick, Julien Dompierre, Marie-Gabrielle Vallet, and Francois Guibault
    "Mesh Smoothing Based on Riemannian Metric Non-Conformity Minimization", Proceedings, 15th International Meshing Roundtable, Springer-Verlag, pp.271-288, September 17-20 2006
    keywords:
    • mesh quality
    • mesh optimization
    • mesh adaptation
    • element size
    • element shape
    • metric comparison
    • boundary orthogonality
    • anisotropy
    • metric
    • smoothing
    Abstract
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Steve L. Karman Jr.
    "Virtual Control Volumes for Two-Dimensional UnstructuredElliptic Smoothing", Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.121-142, October 3-6 2010
    keywords:
    • Unstructured elliptic smoothing
    • Winslow smoothing
    • Finite-volume controlvolume
    • Mesh quality improvement
    Abstract
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Thompson, David S., Satish Chalasani, Bharat K. Soni
    "Generation of Volume Meshes by Extrusion from Surface Meshes of Arbitrary Topology", Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.385-393, October 2000
    keywords:
    • hybrid meshes
    • elliptic smoothing
    • Winslow smoothing
    • smoothing
    • structured
    • advancing layer
    Abstract
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Tournois, Jane, Pierre Alliez, and Olivier Devillers
    "Interleaving Delaunay Refinement and Optimization for 2D Triangle Mesh Generation", Proceedings, 16th International Meshing Roundtable, Springer-Verlag, pp.83-101, October 14-17 2007
    keywords:
    • 2D triangle mesh generation
    • Delaunay refinement
    • optimization
    • mesh smoothing
    • bounded Voronoi diagram.
    Abstract
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Vartziotis, Dimitris and Benjamin Himpel
    "Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes", 22nd International Meshing Roundtable, Springer-Verlag, pp.293-311, October 13-16 2013
    keywords:
    • smoothing
    • quality metric
    • quality measure
    • finite element method
    • global optimization
    • optimization-based method
    • GETMe
    Abstract
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Wang, Jun and Zeyun Yu
    "A Novel Method for Surface Mesh Smoothing:Applications in Biomedical Modeling", Proceedings, 18th International Meshing Roundtable, Springer-Verlag, pp.195-210, October 25-28 2009
    keywords:
    • Surface mesh smoothing
    • Quadric surface fitting
    • Curvature labeling
    • Meshquality improvement.
    Abstract
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Xu, Jing and Andrey N. Chernikov
    "Automatic curvilinear quality mesh generation driven by smooth boundary and guaranteed fidelity", 23rd International Meshing Roundtable, Elsevier Ltd., October 12-15 2014
    keywords:
    • mesh generation
    • high-order
    • Bezier polynomial basis
    • smoothness
    Abstract
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Zhang, Yongjie, Chandrajit Bajaj, and Guoliang Xu
    "Surface Smoothing and Quality Improvement of Quadrilateral/Hexahedral Meshes with Geometric Flow", Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.449-468, September 11-14 2005
    keywords:
    • quadrilateral
    • hexahedra
    • surface smoothing
    • feature preservation
    • quality improvement
    • geometric flow
    Abstract
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Zhou, Tian and Kenji Shimada
    "An Angle-Based Approach to Two-Dimensional Mesh Smoothing", Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.373-384, October 2000
    keywords:
    • smoothing
    • average angle
    • Laplacian
    • optimization-based
    • triangule
    • quadrilateral
    Abstract
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