Meshing Papers, 1993-2002

Center for Computing Research

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.”

Thurston’s post is saved on David Eppstein’s website:
Geometry in Action email Re: Hexahedral decomposition of polyhedra.


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 


Connectivity-Based, All-hexahedral Mesh Generation Method and Apparatus (patent)

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 Captures the Global Connectivity of an All-Hexahedral Finite Element Mesh

Peter Murdoch, Steven Benzley, Ted Blacker, and Scott A. Mitchell

pdf


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

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


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


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


Method for Generating a Mesh Representation of a Region Characterized by a Trunk and a Branch thereon (patent)

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


Cleave and Fill Tool: An All-hexahedral Refinement Algorithm for Swept Meshes

Michael Borden, Steven Benzley, Scott A. Mitchell, David R. White and Ray MeyersProc. 9th International Meshing Roundtable, Sandia National Laboratories, pp. 69-76, October 2000

pdf and IMR

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



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


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


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 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

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


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


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


An Aspect Ratio Bound for Triangulating a d-Grid Cut by a Hyperplane

Scott A. Mitchell and Steven A. VavasisProc. 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


Cubit software demonstration

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

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 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 WhiteSandia National Laboratories, Albuquerque, NM, 1994. SAND94-1100.

pdf