Mesh Generation for High Performance Computing: Current Trends and Applications
Scott A. Mitchell | |
| Address |
Sandia National Laboratories P.O. Box 5800 Mail Stop 0847 Albuquerque, NM 87185-0847 |
| Phone | 505-845-7594 |
| Fax | 505-844-9297 |
| samitch@sandia.gov | |
| URL | http://endo.sandia.gov/~samitch/ |
| Education | Ph.D. Applied Mathematics, Cornell University, 1993 M.S. Applied Mathematics, Cornell University, 1991 B.S., Applied Mathematics, Engineering & Physics, University of Wisconsin-Madison, 1988. |
| Ph.D Thesis | "Mesh Generation with Provable Quality Bounds", S. A. Vavasis, 1993 |
| Positions | Senior Member Technical Staff, Parallel Computing Sciences Department,
Sandia National Laboratories, 1994-present. Limited Term Employee, Applied and Numerical Mathematics Department, Sandia National Laboratories, 1992-1994 Summer Research Intern, Xerox PARC, 1991 |
Statement of Current WorkMy research area is unstructured mesh generation. I've worked on triangulation algorithms, and, since 1995, on hexahedral mesh generation algorithms and toolkit control & automation within the CUBIT software.I’ve worked on Grafting and ensuring the sweepability of volumes. The Whisker Weaving (WW) algorithm generates all-hex meshes of general geometries. Similar to WW, I've written a proof of the existence of topologically well-defined hex meshes. I've developed a number of hex mesh connectivity-improvement algorithms. I discovered the all-hex geode-template, which allows a conforming transition between a diced hexahedral mesh and a tetrahedral mesh. I've also worked on choosing corners for mapped meshing, and a high fidelity scheme for assigning the number of mesh edges on each curve so that each surface may be meshed according to its prescribed. I’ve addressed some CUBIT usability issues and helped create some <>>7 million element hex meshes of complicated CAD assemblies. For my triangulation algorithms, I prove that the algorithms always work, and prove bounds on the number of triangles produced and their shape. I've also explored the tradeoff between number of triangles and the smallest triangle angle. Steve Vavasis, my Ph.D. advisor, has implemented a robust octree-based tetrahedral mesh generator, QMG, based on my thesis work. Selected PublicationsThe Graft Tool: an all-hexahedral transition algorithm for creating a multi-directional swept volume mesh, S. R. Jankovich, S. E. Benzley, J. F. Shepherd, S. A. Mitchell, Proc. 8th International Meshing Roundtable `99, 387-392 (1999). Reliable Whisker Weaving via curve contraction, N. T. Folwell, S. A. Mitchell, Proc. 7th International Meshing Roundtable `98, 365-378, (1998). The all-hex geode-template for conforming a diced tetrahedral mesh to any diced hexahedral mesh , S. A. Mitchell, Proc. 7th International Meshing Roundtable `98, 295-305 (1998), and Engr. with Computers, 15: 228-235. High fidelity interval assignment, S. A. Mitchell, Proc. 6th International Meshing Roundtable `97, 33-44 (1997), and Internation Journal of Computational Geometry and Applications. A global optimization approach to quadrilateral meshing, J. Jung, C. Dohrmann, W. Witkowski, P. Wolfenbarger, W. Gerstle, S. Mitchell, M. Panthaki, D. Segalman, Proc. 6th Int. Meshing Roundtable `97, 155-167 (1997). Choosing corners of rectangles for mapped meshing, S. A. Mitchell, Proc. Thirteenth annual symposium on Computational Geometry, 87-93 (1997). Forming and resolving wedges in the spatial twist continuum, T. D. Blacker, S. A. Mitchell, T. J. Tautges, P. Murdoch, S. Benzley, Engineering with Computers 13:35-47 (1997). The Whisker Weaving Algorithm: a connectivity based method for constructing all-hexahedral finite element meshes, T. J. Tautges, T. D. Blacker, S. A. Mitchell, Int. J. Numer. Methods Engrg. 39:19 (1996), pp. 3327-3350. A characterization of the quadrilateral meshes of a surface which admit a compatible hexahedral mesh of the enclosed volume, S. 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. The spatial twist continuum: a connectivity based method for representing all-hexahedral finite element meshes, P. Murdoch, S. Benzley, T. D. Blacker, S. A. Mitchell, submitted to Int. J. Numer. Methods Engrg. (1995). Pillowing doublets: refining a mesh to ensure that faces share at most one edge, S. A. Mitchell, T. J. Tautges, Proc. 4th International Meshing Roundtable, 231-240 (1995). Cardinality Bounds for Triangulations with Bounded Minimum Angle, S. A. Mitchell, Sixth Canadian Conference on Computational Geometry (1994), 326-331. Linear-Size Nonobtuse Triangulation of Polygons, M. Bern, S. A. Mitchell and J. Ruppert, 10th Annual Symposium on Computational Geometry (1994), 121-130. Refining a Triangulation of a Planar Straight-Line Graph to Eliminate Large Angles, S. A. Mitchell, Thirty-fourth Annual Symposium on Foundations of Computer Science (FOCS '93), 583-591. Quality Mesh Generation in Three Dimensions, S. A. Mitchell and S. A. Vavasis, Proc. 8th Annual Symposium on Computational Geometry (1992), 212-221. Also presented a two-dimensional implementation at the 1991 SUNY Stony Brook Workshop on Computational Geometry. Also Cornell CTC92TR104 9/92 and Cornell CS TR 92-1327 (thesis). PatentsAll-Hex Geode-Template: Mesh Generation and Apparatus, U.S. Patent Pending, 1999. Whisker Weaving : Connectivity-Based, All-Hexahedral Mesh Generation and Apparatus, U.S. Patent 5,768,156. 1998. Professional ActivitiesConference Chair, 5th International Meshing Roundtable, October 1996. Session Chair, International Meshing Roundtable, 1995, 1997, 1998, and 1999. Committee Member, Sixteenth Annual Symposium on Computational Geometry, June 2000. Session Chair, U.S. National Congress on Computational Mechanics, August 1999 Honors, Awards, MembershipAssociation for Computing Machinery (ACM). Phi Beta Kappa Tau Beta Pi | |
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