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Mark S. Shephard

 Professor of Engineering
Mechanical Engineering, Aeronautical Engineering & Mechanics, Rensselaer Polytechnic Institute
Web Page: http://www.meche.rpi.edu/faculty/member/shephard.html
E-mail: shephard@scorec.rpi.edu

MESHING
RESEARCH
CORNER

Baehmann, Peggy L, and Mark S. Shephard

    "Adaptive Multiple-Level h-Refinement in Automated Finite Element Analysis", Engineering With Computers, Springer-Verlag, Num 5, pp.235-247, 1989
    keywords:
    • adaptivity
      		•
    • finite elements
    • numerical models
      		•

Baehmann, Peggy L, Scott L. Wittchen, Mark S. Shephard, Kurt R. Grice and Mark A. Yerry
    "Robust, Geometrically Based, Automatic Two-Dimensional Mesh Generation", International Journal for Numerical Methods in Engineering, Wiley, Vol 24, pp.1043-1078, 1987
    keywords:
    • quadrilateral
      		•
    • quadtree
    • triangle
      		•
    Abstract

Beall, Mark W., Joe Walsh and Mark S. Shephard
    "Accessing CAD geometry for mesh generation", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.33-42, Sept. 2003
    keywords:
    • CAD
      		•
    • geometric tolerances
    • geometry management
      		•
    • topology
    • unified topology model
      		•
    Abstract
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Beall, Mark W., Shephard, Mark S.
    "A General Topolpgy-Based Mesh Data Structure", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 40, Num 9, pp.1573 - 1596, May 1997
    keywords:
    • hierarchic
      		•
    • mesh data structures
    • topology
      		•
    Abstract

De Cougny, H. L. and M. S. Shephard
    "Parallel Refinement and Coarsening of Tetrahedral Meshes", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Num 46, pp.1101-1125, November 1999
    keywords:
    • adaptive
      		•
    • coarsening
    • parallel
      		•
    • refinement
    Abstract

de Cougny, H. L. and M. S. Shephard
    "Refinement, Derefinement, and Optimization of Tetrahedral Geometric Triangulations in Three Dimensions", Draft, 1995
    keywords:
    • clean-up
      		•
    • coarsening
    • derefinement
      		•
    • improvement
    • optimization
      		•
    • refinement
    • tetrahedron
      		•
    • topology
    Abstract

de Cougny, H. L. and M. S. Shephard
    "Surface Meshing Using Vertex Insertion", 5th International Meshing Roundtable, Sandia National Laboratories, pp.243-256, October 1996
    keywords:
    • curvature
      		•
    • parametric surface
    • quality
      		•
    • surface meshning
    • triangle
      		•
    • validity
    Abstract
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Dey, S., R. M. O'Bara and M. S. Shephard
    "Towards curvilinear meshing in 3D: the case of quadratic simplices", Computer Aided Design, Elsevier, Vol 33, Num 3, pp.199-209, March 2001
    keywords:
    • Curvilinear mesh generation; p-Version analysis
      		•
    • coarse meshing
    Abstract

Dey, Saikat, Mark S. Shephard and Marcel K. Georges
    "Elimination of the Adverse Effects of Small Model Features by the Local Modification of Automatically Generated Meshes", Engineering with Computers, 1995
    keywords:
    • geometry management
      		•
    • small features
    • dirty geometry
      		•
    • octree
    Abstract

Dey, Sailkat, Robert M. O'Bara and Mark S. Shephard
    "Curvilinear Mesh Generation in 3D", Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.407-417, October 1999
    keywords:
    • tetrahedra
      		•
    • coarse mesh
    • curvilinear mesh generation
      		•
    • computational geometry
    • p-version analysis
      		•
    Abstract
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Garimella, Rao and Mark S. Shephard
    "Tetrahedral Mesh Generation With Mutliple Elements Through the Thickness", Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.321-333, October 1995
    keywords:
    • octree
      		•
    • tetrahedron
    Abstract
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Garimella, Rao V. and Mark S. Shephard
    "Boundary Layer Meshing for Viscous Flows in Complex Domains", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.107-118, October 1998
    keywords:
    • tetrahedra
      		•
    • boundary layer
    • CFD
      		•
    • anisotropy
    • advancing layers
      		•
    Abstract
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Garimella, Rao V. and Mark S. Shephard
    "Boundary layer mesh generation for viscous flow simulations", International Journal for Numerical Methods in Engineering, John Wiley, Vol 49, Num 1, pp.193-218, September 10-20 2000
    keywords:
    • anisotropy
      		•
    • boundary layers
    • hybrid
      		•
    • advancing layers
    • CFD
      		•
    Abstract

Garimella, Rao V. and Mark S. Shephard
    "Mesh Quality and Control in Boundary Layer Mesh Generation for Viscous Flows", 2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999
    keywords:
    • CFD
      		•
    • boundary layer
    • advancing layers
      		•
    • gradation
    • size control
      		•
    Abstract

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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Karamete, B. Kaan, Mark W. Beall and Mark S. Shephard
    "Triangulation of arbitrary polyhedra to support automatic mesh generators", International Journal for Numerical Methods in Engineering, John Wiley, Vol 49, Num 1, pp.167-191, September 10-20 2000
    keywords:
    • surface meshing
      		•
    • face recovery
    • Delaunay
      		•
    • robustness
    • boundary conforming
      		•
    Abstract

Karamete, B. Kaan, Mark W. Beall and Mark S. Shephard
    "Triangulation of Arbitrary Polyhedra", 2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999
    keywords:
    • tetrahedra
      		•
    • polyhedra
    • non-convex polyhedra
      		•
    • boundary recovery
    • Delaunay
      		•
    • boundary constrained
    Abstract

Karamete, B. Kaan, Rao V. Garimella and Mark S. Shephard
    "Edge Recovery Method on an Existing Surface Mesh for Boundary Layer Meshing", 2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999
    keywords:
    • boundary layer
      		•
    • edge recovery
    • surface meshing
      		•
    • triangle
    Abstract

Karamete, B. Kaan; Garimella, Rao V.; Shephard, Mark S.
    "Recovery of an arbitrary edge on an existing surface mesh using local mesh modifications", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 50, Num 6, pp.1389 - 1409, February 2001
    keywords:
    • edge recovery
      		•
    • unstructured
    Abstract

Li, Xiangrong, Jean-Francois Remacle, Nicolas Chevaugeon and Mark S. Shephard
    "Anisotropic Mesh Gradation Control", Proceedings, 13th International Meshing Roundtable, Williamsburg, VA, Sandia National Laboratories, SAND #2004-3765C, pp.401-412, September 19-22 2004
    keywords:
    • tensor field
      		•
    • anisotropic
    • gradation
      		•
    • adaptation
    • sizing function
      		•
    Abstract
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Li, Xiangrong; Shephard, Mark S.; Beall, Mark W.
    "Accounting for curved domains in mesh adaptation", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 58, Num 2, pp.247-276, July 2003
    keywords:
    • mesh modification
      		•
    • mesh refinement
    Abstract

Remacle, Jean-Francois, Ottmar Klaas, Joseph E. Flaherty and Mark S. Shephard
    "Parallel Algorithm Oriented Mesh Database", Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.197-206, October 7-10 2001
    keywords:
    • parallel
      		•
    • mesh database
    • adaptivity
      		•
    • load balancing
    • library
      		•
    • data structure
    • API
      		•
    • object-oriented
    Abstract
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Remacle, Jean-Francois, B. Kaan Karamete and Mark S. Shephard
    "Algorithm Oriented Mesh Database", Proceedings, 9th International Meshing Roundtable, Sandia National Laboratories, pp.349-359, October 2000
    keywords:
    • data structure
      		•
    • database
    • AOMD
      		•
    • STL
    Abstract
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Remacle, Jean-François; Shephard, Mark S.
    "An algorithm oriented mesh database", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 58, Num 2, July 2003
    keywords:
    • C++STL
      		•
    • mesh database
    • mesh representation
      		•
    Abstract

Schroeder, W.J. and M.S. Shephard
    "A Combined Octree/Delaunay Method For Fully Automatic 3-D Mesh Generation", International Journal For Numerical Methods in Engineering, John Wiley, Num 29, pp.37-55, 1990
    keywords:
    • Delaunay
      		•
    • finite elements
    • octree
      		•
    • triangulation

Schroeder, W.J. and M.S. Shephard
    "Geometry-Based Fully Automatic Mesh Generation and the Delaunay Triangulation", International Journal For Numerical Methods in Engineering, John Wiley, Num 26, pp.2503-2515, 1988
    keywords:
    • Delaunay
      		•
    • finite elements
    • tetrahedron
      		•
    • triangulation

Schroeder, W.J., M.S. Shephard
    "An O(N) Algorithm to Automatically Generate Geometric Triangulations Satisfying the Delaunay Circumsphere Criteria", Engineering With Computers, Springer-Verlag, Num 5, pp.177-193, 1989
    keywords:
    • Delaunay triangulation
      		•
    • octree
    • three dimensional
      		•

Schroeder, William J. and Mark S. Shephard
    "On Rigorous Conditions for Automatically Generating Finite Element Meshes", Product Modeling for Computer-Aided Design and Manufacturing, Elsevier, pp.267-281, 1991
    keywords:
    • quality
      		•
    • octree
    • criteria
      		•
    • data structures
    • mesh criteria
      		•
    Abstract

Shephard M. S., S. Dey, J. E. Flaherty
    "A straightforward structure to construct shape functions for variable p-order meshes", Computer Methods in Applied Mechanics and Engineering, Elsevier, Vol 147, pp.209-233, 1997
    keywords:
    • p-method
      		•
    Abstract

Shephard Mark S, Saikat Dey and Marcel K. Georges
    "Automatic Meshing of Curved Three-Dimensional Domains: Curving Finite Elements and Curvature-Based Mesh Control", Proceedings of the IMA Swnmer program Modeling, Mesh Generation, and Adaptive Numerical Method for Partial Differential Equations, Springer-Verlag, July 1993
    keywords:
    • surface meshing
      		•
    • curvature
    • triangles
      		•
    • geometric evaluation
    • octree
      		•
    • nodal spacing
    Abstract

Shephard, M.S. and J.A. Lo
    "Automatic generation of Coarse Three-dimensional Meshes Using the Functionality of a Geometric Modeler", Advances in Engineering Software, Elsevier, Vol 56, Num 13, pp.273-286, 1991
    keywords:
    • finite elements
      		•
    • three-dimensional

Shephard, M.S., F. Guerinoni, J.E. Flaherty, R.A. Ludwig and P.L. Baehmann
    "Finite Octree Mesh Generation for Three-Dimensional Flow Analysis", Numerical Grid Generation in Computational Fluid Mechanics `88, Pineridge Press, pp.709-718, 1988
    keywords:
    • octree
      		•
    • tetrahedra
    • finite volume
      		•
    • finite octree technique
    Abstract

Shephard, M.S., M.W. Beau and R.M. O'Bara
    "Revisiting the Elimination of the Adverse Effects of Small Model Features in Automatically Generated Meshes", Proceedings, 7th International Meshing Roundtable, Sandia National Lab, pp.119-132, October 1998
    keywords:
    • tetrahedra
      		•
    • small features
    • feature supression
      		•
    • geometry management
    Abstract
    Download Full Paper (Postscript Format)

Shephard, Mark S
    "Update to: Approaches to the automatic generation and control of finite element meshes", Appl Mech Rev, ASME, Vol 49, Num 10, pp.S5-S14, October 1996
    keywords:
    • anisotropy
      		•
    • CAD
    • classification
      		•
    • hexahedra
    • improvement
      		•
    • overview
    • parallel
      		•
    • tetrahedra
    Abstract

Shephard, Mark S and Marcel K. Georges
    "Automatic Three-Dimensional Mesh Generation by the Finite Octree Technique", International Journal for Numerical Methods in Engineering, Wiley, Vol 32, pp.709-749, 1991
    keywords:
    • octree
      		•
    • tetrahedra
    Abstract

Shephard, Mark S.
    "Automatic and Adaptive Mesh Generation", IEEE Transactions on Magnetics, IEEE, Vol 6, Num 21, pp.2484-2489, Nov. 1985
    keywords:
    • adaptivity
      		•
    • finite elements
    • three-dimensional
      		•
    • two-dimensional

Shephard, Mark S.
    "Finite Element Modeling Within an Integrated Geometric Modeling Environment: Part I--Mesh Generation", Engineering With Computers, Springer-Verlag, Num 1, pp.61-71, 1985
    keywords:
    • finite elements
      		•
    • geometric modeling

Shephard, Mark S.
    "Meshing environment for geometry-based analysis", International Journal for Numerical Methods in Engineering, John Wiley & Sons, Ltd., Vol 47, Num 1, pp.169 - 190, January 2000
    keywords:
    • meshing tools
      		•
    Abstract

Shephard, Mark S. and Marcel K. Georges
    "Reliability of automatic 3D mesh generation", Computer Methods in Applied Mechanics and Engineering, North-Holland, Vol 101, pp.443-462, 1992
    keywords:
    • data structure
      		•
    • criteria
    • mesh criteria
      		•
    • reliability
    • robustness
      		•
    • octree
    • geometry evaluation
      		•
    Abstract

Shephard, Mark S. and Peter M. Finnigan
    "Toward Automatic Model Generation", State-of-the-Art Surveys on Computational Mechanics, eds. Ahmed K. Noor and J. Tinsley Oden, ASME, Vol 11, pp.335-366, 1991
    keywords:
    • data structure
      		•
    • overview
    • octree
      		•
    • tetrahedra
    • artificial intelligence
      		•
    Abstract

Wan, Jie, Suleyman Kocak and Mark S. Shephard
    "Automated adaptive forming simulations", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.323-334, Sept. 2003
    keywords:
    • adaptive mesh control
      		•
    • metal forming
    • adaptivity
      		•
    Abstract
    Download Full Paper (Postscript Format)

Yerry, Mark A. and Mark S. Shephard
    "Trends in Engineering Software and Hardware: Automatic Mesh Generation for Three-Dimensional Solids", Computers and Structures, Pergammon, Vol 20, Num 1, pp.31-39, 1985
    keywords:
    • octree
      		•
    • tetrahedra
    Abstract

Yerry, Mark A. and Mark S. Shephard
    "Automatic Three-Dimensional Mesh Generation By The Modified Octree Technique", International Journal For Numerical Methods in Engineering, John Wiley, Num 20, pp.1965-1990, 1984
    keywords:
    • finite elements
      		•
    • octree
    • tetrahedron
      		•
    • three-dimensional

Yin, Luzhong, Xiaojuan Luo, Mark S. Shephard
    "Identifying and Meshing Thin Sections of 3-d Curved Domains", Proceedings, 14th International Meshing Roundtable, Springer-Verlag, pp.33-54, September 11-14 2005
    keywords:
    • thin sections
      		•
    • medial surface
    • prismatic elements
      		•
    Abstract
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