Tim's Papers and Presentations

What fun would research be if we couldn't tell others about it?  Below are some of the things I've worked on in the recent past, and papers I've written or presentations I've made on the subjects.  Order is chronological within topics, sort of, with active topics listed first.

Dual-Based Hexahedral Mesh Modification

I've been interested in this problem since the early days of my work on whisker weaving.  However, I owe it to David Eppstein's presentation at the 10th IMR for getting me interested in the subject again.  Since starting work on this in Fall '01, I've published/presented the following.

Timothy J. Tautges, "A Set of  Atomic, Dual-Based Operations for Modifying Hexahedral Mesh Topology", presentation to UW-Madison Math Dept. Topology Group, April 16, 2004.
I wouldn't list this one, except that it's the most comprehensive presentation on this work to date.

Timothy J. Tautges, Sarah E. Knoop, “Combinatorial Aspects of Dual-Based Hexahedral Mesh Modification”, SIAM Workshop on Combinatorial Scientific Computing, San Francisco, CA, Feb. 27-28, 2004.
Extended abstract, describing two operations (atomic pillow and face open/collapse) which (I thought were) sufficient for describing Bern et. al's flipping operations.  One of these days I'll figure out whether it's two or three...

Timothy J. Tautges, Sarah E. Knoop, "Topology modification of hexahedral meshes using atomic dual-based operations", Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories report SAND 2003-3030P, pp.415-423, Sept. 2003.

My first publication on the subject.  Most interesting part of the published paper was a proof that the dual of a hex mesh is a simple polytope complex and also a simple arrangement (pictures at right are hints on how the proof went).  I've been told that this hadn't been proven before, though I'd have thought it would have been.  There's an offhand reference to the fact in Grunbaum (see ref in this paper), but that's all I've seen on the subject.  If you know of any other proofs (or even just statements), I'd love to hear them.

TSTT / Mesh, Geometry Components & Interfaces

I've been part of the Terascale Simulation Tools & Technologies center, a project funded by DOE Office of Science's SciDAC program.  This work has been fun for many reasons, including being able to work with lots of other researchers in the field outside Sandia, seeing some pretty complicated meshing problems, and developing my ideas on interoperable software components related to mesh generation.

Timothy J. Tautges, Ray Meyers, Karl Merkley, Clint Stimpson, Corey Ernst, “MOAB: A Mesh-Oriented Database”, Sandia National Laboratories, SAND2004-1592, Albuquerque, NM, April 2004.
Hot off the press.  User's Guide for MOAB, including design philosophy and data model.  This is a good place to start if you want to use MOAB.  Includes 3 "getting started" examples which demonstrate usefulness of the data model in MOAB.

Timothy J. Tautges, “MOAB-SD: Integrated Structured and Unstructured Mesh Representation”, Engineering With Computers, 20, 286-293 (2004).

A method of representing globs of structured and semi-structured (swept) mesh which share mesh interfaces, where that shared interface can live in the parametric space of both globs (and optionally its own).  Eliminates need to store connectivity array, saving about 57% of mesh storage space compared to unstructured representation. 

Ray J. Meyers, Karl Merkley, Timothy J. Tautges, “SNL Implementation of the TSTT Mesh Interface”, 8th International Conference on Numerical Grid Generation in Computational Field Simulations, Honolulu, HA, June 2-6, 2002.

Early publication of many of the principles behind MOAB.  Mostly qualitative, little data.

Timothy J. Tautges, Steven J. Owen, “Coupling of Smooth Faceted Surface Evaluations in the SIERRA FEA Code”, 5th World Congress on Computational Mechanics, Vienna, Austria, July 9, 2002.
Paper descibing my method for evaluating h-refined quadrilaterals based on triangular facet-based smooth surface approximation.  One interesting thing I showed and implemented was the 6 arrangements of quads with 0-4 edges refined decomposed into triangles which resolved all mid-edge nodes (2 of them shown at right).  If you don't understand how that could possibly be done, you're in good company.  This talk was part of the Symposium on Computational Geometry for Mechanics & Applications I arranged as part of the 5th WCCM in Vienna, Austria.  Included here because it's a good example of using components.

Hexahedral Mesh Generation (and other stuff)

David R. White, Timothy J. Tautges, "Automatic Scheme Selection for Toolkit Hex Meshing", Int. J. Numer. Meth. Engr., 49, 127-144 (2000).

By far my highest-impact work.  A person once told me you couldn't figure out whether a volume could be swept until you meshed the surfaces of that volume.  That's a sure way to motivate me to do something.  As it turns out, you only need to assign corners on linking surfaces, surface mesh schemes, and intervals (see paper for details).  David White implemented this work, and it's still one of the most-used algorithms in CUBIT.  Sweep group detect also came from this work (also important in assembly meshing).

Timothy J. Tautges, "The Generation of Hexahedral Meshes for Assembly Geometries: Survey and Progress", Int. J. Numer. Meth. Eng, 50, 2617-2642 (2001).
Little-noticed survey paper on hex meshing state of the art, first presented as keynote address at 2nd Trends in Unstructured Mesh Generation meeting.  Not much has changed in practice since this was written.  Figure at the right is from the second of the CUBIT team's heroic meshing jobs (the NG tube), which benefitted from lots of the developments described in this paper and which were inspired from the first of our heroic meshing jobs (the NG power supply).

T. J. Tautges, T. Blacker and S. A. Mitchell, 'The Whisker Weaving Algorithm: A Connectivity-Based Method for Constructing All-Hexahedral Finite Element Meshes', Int. J. Numer. Meth. Eng., 39, 3327-3349 (1996).
By far my most-referenced paper.  Still worth thinking about, though it's far from bulletproof.  Scott Mitchell's work on curve contraction-based whisker weaving is another and possibly better approach to doing dual-based hex meshing (don't tell him I told you that though!)

Geometry Stuff

Geometry & CAD, Short Course Notes, 12th International Meshing Roundtable, Santa Fe, NM, Sept. 13, 2003.
Notes from the short course I gave.  Not included in these notes, but an important part of my presentation, was an overview of subdivision surfaces.  Most of that was cribbed (with permission) from Denis Zorin's SigGraph 99 presentation on the subject.

Timothy J. Tautges, “CAD Interfaces: Why Simple Wrappers Aren't Enough”, invited presentation, SIAM Conference on Computational Science and Engineering (CSE03), San Diego, CA, February 12, 2003.

Title says it all.  Abstract only, so links are to slides presented at conference.

Timothy J. Tautges, “CAD-based Monte Carlo Simulation Using MCNP-X and CGM”, Seminar, Los Alamos National Laboratory, December 18, 2002.
Another interesting use of CAD (and other) geometry, for monte carlo calculations.  One of the few opportunities to use my experience in mesh generation with my training as a Nuclear Engineer.

Timothy J. Tautges, “Automatic Detail Reduction for Mesh Generation Applications”, Proceedings, 10th International Meshing Roundtable, SAND2001-2976C, Sandia National Laboratories, pp. 407-418, October 2001.
This area is quite important, but doesn't receive much attention from the mesh generation research world.  My view: automatic detail suppression for mesh generation is a meshing-time decision, and should be automatic with the option for user control.  This paper has interesting things to say about both the detection and removal of small details.  Here I introduced using hydraulic diameter for measuring characteristic size, which is more effective at indicating small details than raw size measures (area, volume, etc.).

Timothy J. Tautges, “Design and Use of Geometry Attributes To Support Mesh Generation and Analysis Applications”,  Symposium on Advances in Software Technology for Computational Mechanics, held in conjunction with the 6th U.S. Conference on Computational Mechanics, Dearborn, MI, August 1-4, 2001.

Describes my design & implementation for embedding attributes in geometry.  Still the basis of saving meshing and other information with geometry in CUBIT (including to support save/restore to/from .cub files).  This work was formative in developing my ideas on tags, used in my TSTT work.

Timothy J. Tautges, “The Common Geometry Module (CGM): a Generic, Extensible Geometry Interface”, Engineering with Computers, 17:3, 299-314 (2001).

In spite of the multiple inheritance that everybody hates (including me), still the best example of a CAD-neutral and topological model-neutral geometry wrapper.  API could use some polishing, but that's coming.

Yong Lu, Rajit Gadh, Timothy J. Tautges, "Feature Based Hex Meshing Methodology: Feature Recognition and Volume Decomposition", Computer-Aided Design, 33 (2001) 221-232.
Good summary of automatic decomposition for hex meshing research.  Not really finished, but still a good start (figure at the right resulted from autodecomposition of single part).  If and when we get a robust all-hexahedral meshing algorithm, this will become more important.