Meshing Papers, 1993-2002


email:  Scott A. Mitchell

 CCR

Dual Hex Meshing, Whisker Weaving

This first paper is informally known as the "hex mesh existence proof"

A Characterization of the Quadrilateral Meshes of a Surface which Admit a Compatible Hexahedral Mesh of the Enclosed Volume
Scott A. Mitchell
Proc. 13th Annual Symposium on Theoretical Aspects of Computer Science (STACS `96), Lecture Notes in Computer Science 1046, Springer, pages 465-476, 1996
pdf
STACS slides pdf

See also David Eppstein's result: Linear complexity hexahedral mesh generation

Bill Thurston also wrote a newsgroup article outlining a proof that is similar to my paper: "Hexahedral decomposition of polyhedra, sci.math, 25 Oct 1993." David Eppstein has a copy of this online.

Reliable Whisker Weaving via Curve Contraction
Nathan T. Folwell and Scott A. Mitchell
Proc. 7th International Meshing Roundtable `98, 365-378, (1998).
pdf 
 bibtex

The Whisker Weaving Algorithm: a Connectivity Based Method for Constructing All-hexahedral Finite Element Meshes
Timothy J. Tautges, Ted D. Blacker, Scott A. Mitchell
Int. J. Numer. Methods Engrg. 39:19 (1996), pp. 3327-3350
pdf and doi

Progress Report on the Whisker Weaving All-hexahedral Meshing Algorithm
Timothy J. Tautges and Scott A. Mitchell
5th International Conference on Numerical Grid Generation in Computational Field Simulations, Mississippi State University, pp.659-670, April 1996
Sandia Tech Library and UNT

Hexahedral Mesh Generation via the Dual
Steven Benzley, Ted D. Blacker, Scott A. Mitchell, Peter Murdoch, Timothy J. Tautges
Proc. 11th Annual Symp. on Computational Geometry, C4-C5 (1995).
ACM digital library 

Patent related to Whisker Weaving

Connectivity-Based, All-hexahedral Mesh Generation Method and Apparatus,
Timothy J. Tautges, Scott A. Mitchell, Ted D. Blacker, and Peter Murdoch.
Patent US 5,768,1556, 16 June 1998. Sandia Corporation, Albuquerque, NM.
pdf

The Spatial Twist Continuum: a Connectivity Based Method for Representing All-hexahedral Finite Element Meshes
Peter Murdoch, Steven Benzley, Ted D. Blacker, and Scott A. Mitchell
Finite Elements in Analysis and Design, Volume 28, Number 2, 15 December 1997, Elsevier, pp. 137-149(13)
pdf

The Spatial Twist Continuum Captures the Global Connectivity of an All-Hexahedral Finite Element Mesh
Peter Murdoch, Steven Benzley, Ted Blacker, and Scott A. Mitchell
pdf

Whisker Weaving: Invalid Connectivity Resolution and Primal Construction Algorithm
Timothy J. Tautges and Scott A. Mitchell
Proceedings, 4th International Meshing Roundtable, SAND95-2130, Sandia National Laboratories, pp.115-127, October 1995.
IMR

Pillowing Doublets: Refining a Mesh to Ensure that Faces Share at Most One Edge
Scott A. Mitchell and Timothy J. Tautges
Proc. 4th International Meshing Roundtable, 231-240 (1995).
IMR
bibtex

Forming and Resolving Wedges in the Spatial Twist Continuum
Ted D. Blacker, Scott A. Mitchell, Timothy J. Tautges, Peter Murdoch, Steven Benzley,
Engineering with Computers 13:35-47 (1997)
pdf and  journal site

Dual-based hex meshing, non-Whisker-Weaving

The Graft Tool: an All-hexahedral Transition Algorithm for Creating a Multi-directional Swept Volume Mesh
Steven R. Jankovich, Steven E. Benzley, Jason F. Shepherd, and Scott A. Mitchell
Proc. 8th International Meshing Roundtable `99, 387-392 (1999)
imr

Patent related to Graft Tool

Method for Generating a Mesh Representation of a Region Characterized by a Trunk and a Branch thereon.
Jason Shepherd, Scott A. Mitchell, Steven R. Jankovich, and Steven E. Benzley.
Patent US 7,219,039 B1, 15 May 2007. Sandia Corporation, Albuquerque, NM. pdf

The All-hex Geode-template for Conforming a Diced Tetrahedral Mesh to any Diced Hexahedral Mesh
Scott A. Mitchell
Proc. 7th International Meshing Roundtable `98, 295-305 (1998), and Engineering with Computers, 15: 228-235.

paper with erroneous mesh node coordinates. Fixed coordinates as txt file and cubit journal file.

The Geode Algorithm: Combining Hex/tet Plastering, Dicing and Transition Elements for Automatic, All-hex Mesh Generation
Robert W. Leland, Darryl J. Melander, Ray W. Meyers, Scott A. Mitchell, Timothy J. Tautges
Proc. 7th International Meshing Roundtable `98, 515-521 (1998).
paper

Cleave and Fill Tool: An All-hexahedral Refinement Algorithm for Swept Meshes
Michael Borden, Steven Benzley, Scott A. Mitchell, David R. White and Ray Meyers
Proc. 9th International Meshing Roundtable, Sandia National Laboratories, pp. 69-76, October 2000
pdf and IMR

Interval assignment and structured cubical meshing

Methods for Multisweep Automation
Jason Shepherd, Scott A. Mitchell, Patrick Knupp, and David White
Proc. 9th International Meshing Roundtable, pp. 77-87, October 2000
pdf and IMR

Interval Assignment for Volumes with Holes
Jason Shepherd, Steven Benzley and Scott A. Mitchell
International Journal for Numerical Methods in Engineering, John Wiley, Vol 49, Num 1, pp. 277-288, 2000
pdf and Sandia Tech Library and OSTI and IJNME and doi

High Fidelity Interval Assignment
Scott A. Mitchell
Proc. 6th International Meshing Roundtable `97, 33-44 (1997), and
International Journal of Computational Geometry and Applications, Vol. 10, No. 4 (2000) 399-415.
journal paper

Choosing Corners of Rectangles for Mapped Meshing
Scott A. Mitchell
Proc. Thirteenth annual symposium on Computational Geometry, 87-93 (1997)
ACM digital library and citeseer

Integration of Mesh Optimization with 3D All-Hex Mesh Generation, LDRD Subcase 3504340000, Final Report, Patrick Knupp and Scott A. Mitchell, SAND99-2852, Unlimited Release, November 1999.
tech report and local mirror, also black&white and ps
bibtex

A Method for Controlling Skew on Linked Surfaces 
R. A. Kerr, S. E. Benzley, D. R. White, S. Mitchell
Proc. 8th International Meshing Roundtable `99, 377- 385 (1999)
pdf and imr
bibtex

An Immersive Environment for Exploration of CUBIT Meshes
C. J. Pavlakos, J. S. Jones, and S. A. Mitchell
Proc. 6th International Meshing Roundtable `97, 47-65 (1997).
imr

A Global Optimization Approach to Quadrilateral Meshing
Joseph Jung, Clark Dohrmann, Walter Witkowski, Paul Wolfenberger, Walter Gerstle, Scott A. Mitchell, Malcolm Panthaki, and Daniel Segalman
Proc. 6th International Meshing Roundtable `97, 155-167 (1997).
imr

An Aspect Ratio Bound for Triangulating a d-Grid Cut by a Hyperplane
Scott A. Mitchell and Steven A. Vavasis
Proc. 12th Annual Symposium on Computational Geometry, (1996) 48-57
citeseer

Courses, demos, and user manuals

A Technical History of Hexahedral Mesh Generation
Scott A. Mitchell
11th International Meshing Roundtable, short course, 15 Sept 2002.
abstract
powerpoint slides

Mesh Generation for High Performance Computing. Part II: Mesh Generation for Massively Parallel-Based Analysis.
Scott Mitchell, Patrick Knupp, and Timothy J. Tautges
Tutorial S6B, Supercomputing 2000.

Cubit software demonstration,
Department of Energy, Accelerated Strategic Computing Initiative (ASCI), SC2000 Research Exhibitor Booth R1124, Supercomputing 2000. 

CUBIT Mesh Generation Enviroment Users Manual, vol. 1
Ted D. Blacker, Steven Benzley, Steven Jankovich, Robert Kerr, Jason Kraftcheck, Robert Kerr, Patrick Knupp, Robert Leland, Darryl Melander, Ray Meyers, Scott A. Mitchell, Jason Shepard, Timothy J. Tautges, and David White
Sandia National Laboratories, Albuquerque, NM, 1994. SAND94-1100.
pdf