Geometric Computing in Science and Engineering
Geometric Computing in Science and Engineering
Geometry is the foundation of many computational methods and applications across diverse spatial scales, ranging from the tiniest carbon nanofibers to the astronomical galaxies. Geometry plays a critical role in the fundamental understanding of physical principles as well as sound engineering designs. Modern applications are experiencing increasingly complex geometry, leading to significant challenges in modeling and simulation of complex physical systems. At the GeoCSE Lab, we strive to develop robust and novel enabling technologies for complex geometric problems in scientific and engineering applications, leveraging techniques across the traditional boundary of computer science and applied mathematics in areas including computational geometry, geometric modeling, linear algebra, numerical differential equations, data analysis, and parallel computing. The current research focus includes tracking dynamic surfaces, coupling in multi-physics analysis, computational mesh processing, high-performance geometric computing, and geometric data analysis. The application areas include solid rocket combustion, fluid-structure interactions, micro- and nano-structures, computer graphics, and medical imaging.
Faculty
Affiliated Ph.D. Students
- Ying Chen
- Bryan Clark
- Volodymyr Dyedov
- Duo Wang
Past Students
- Ankita Jain (GaTech, MS in 2007, now at Cisco Systems)
- Narasimha (Rao) Bayyana (GaTech, MS in 2007 )
- Phil Alexander (UIUC, MS in 2005, now with UIUC)
- Tyler J. Alumbaugh (UIUC, MS in 2005, now with Lawrence Livermore National Laboratory)
Blasting-off rockets, flapping wings, beating hearts, floating bubbles, growing carbon nanotube... The world is full of moving objects at different temporal and spatial scales, and their modeling and simulation requires sophisticated technology to represent their dynamic shapes accurately and efficiently. Many computational problems can also be formulated and solved using moving-surface techniques. However, tracking complex moving surfaces is a very challenging problem. Popular methods include the level-set methods, which are relatively simple to implement but may suffer from insufficient accuracy for scientific applications, and front-tracking methods, which may be more accurate but are more difficult to be made robust. We are developing efficient and robust algorithms for tracking moving surfaces through a new unified theoretical framework and novel computational methods.
Publications:
- X. Jiao, N.R. Bayyana, and H. Zha, Optimizing Surface Triangulation via Near Isometry with Reference Meshes, in Proceedings of International Conference on Computational Science 2007, Beijing, May 2007.
- X. Jiao, Face offsetting: a unified framework for explicit moving interfaces. Journal of Computational Physics, Vol 220(2), pages 612–625, 2007.
- X. Jiao, A. Colombi, X. Ni, and J. Hart, Anisotropic mesh adaptation for evolving triangulated surfaces. in Proceedings of 15th International Meshing Roundtable, Birmingham AL, September 2006.
- R.S. Bellur Ramaswamy, E. Fried, X. Jiao, and D.A. Tortorelli, Simulating solid-solid phase transition in shape-memory alloy microstructure by face-offsetting method, in Multiscale and Functionally Graded Materials Conference 2006
- X. Jiao et al., Accurate and efficient tracking of moving interfaces using face offsetting and anisotropic mesh adaptation, In preparation for International Journal for Numerical Methods in Engineering, 2006.
- Sample movies: "Enright test" (
2MB,
5MB), sphere in vortex (
- X. Jiao et al, Constrained surface propagation and its applications in solid-rocket combustion. In preparation.
- Sample movies: Burning solid-propellant rocket under nonlinear constraints: full rocket (
- X. Jiao, Sliding and colliding: moving interfaces under equality and inequality constraints. In preparation.
Software:
- Surfprop: A robust implementation of face-offsetting with anisotropic mesh adaptation.
Past students:
- R.S. Bellur Ramaswamy (with Dan Tortorelli, UIUC)
Multi-physics, multi-scale modeling is the holy grail of computational science. Spatial and temporal coupling of multi-physics requires rigorous numerical methods supported by efficient geometric data structures and algorithms. We have developed the state-of-the-art geometric algorithms for correlating different meshes by constructing a common refinement of the meshes and advanced numerical methods for data transfer in multi-physics coupling. We have demonstrated significant advantages of our methods in fluid-structure interactions compared with the prior state of the art. We are currently further enhancing the robustness of our geometric algorithms for pathological cases and exploring efficient and stable techniques on temporal coupling.
Publications:
- A. Jain and X. Jiao, Enhancement of mesh overlay for surfaces with non-matching features, in preparation, 2007.
- R. K. Jaiman, P. H. Geubelle, E. Loth, and X. Jiao, Stable and Accurate Loosely-Coupled Scheme for Unsteady Fluid-Structure Interaction, Journal of Computational Physics, submitted, 2007.
- R. K. Jaiman, X. Jiao, P. H. Geubelle, and E. Loth. Conservative load transfer along curved fluid-solid interface with non-matching meshes. Journal of Computational Physics. Vol 218(1), pages 372-397, 2006.
- R. K. Jaiman, X. Jiao, P. H. Geubelle, and E. Loth. Assessment of conservative load transfer for fluid-solid interface with non-matching meshes. International Journal for Numerical Methods in Engineering. Vol 64(15), pages 2014-2038, 2005.
- X. Jiao and M. T. Heath. Common-refinement-based data transfer between nonmatching meshes in multiphysics simulations. International Journal for Numerical Methods in Engineering. Vol 61(14), pages 2402-2427. December 2004.
- X. Jiao and M. T. Heath. Overlaying surface meshes, part i: algorithms. International Journal on Computational Geometry and Applications. Vol 14(6), pages 379-402. December 2004.
- X. Jiao and M. T. Heath. Overlaying surface meshes, part ii: topology preservation and feature matching. International Journal on Computational Geometry and Applications. Vol 14(6), pages 403-419. December 2004.
- X. Jiao and M. T. Heath. Efficient and robust algorithms for overlaying surface meshes. In Proceedings of 10th International Meshing Roundtable. October 2001.
- X. Jiao, H. Edelsbrunner and M. T. Heath. Mesh association: formulation and algorithms. In Proceedings of 8th International Meshing Roundtable. October 1999.
Software:
- Surfdiver: A software for constructing the common refinement of surface meshes.
Past students:
Finite-element or finite-volume analysis requires high-quality computational meshes. Although mature commercial tools are available for generating initial meshes, analysis and adaptation computational meshes within numerical simulation codes still poses significant challenges, especially for surface meshes with complex geometry. Our focus are primarily on feature detection and mesh optimization of surface meshes.
Publications:
- X. Jiao and H. Zha, Normal and Curvature Estimation Using Face-Based Quadratic Fittings for General Surface Meshes, submitted, 2007.
- X. Jiao and N.R. Bayyana, Identification of C1 and C2 Discontinuities for Surface Meshes in CAD, Computer-Aided Design, submitted, 2007.
- Sample results: Boeing new airplane (cockpit, nacelle, nozzle, courtesy of Boeing), Falcon aircraft, fandisk, complex part, fan
- X. Jiao, Volume and feature preservation in surface mesh optimization. in Proceedings of 15th International Meshing Roundtable, Birmingham AL, September 2006.
- T.J. Alumbaugh and X. Jiao, Compact array-based mesh data structures. In 14th International Meshing Roundtable, San Diego, September 2005.
- X. Jiao and P. Alexander, Parallel feature-preserving mesh smoothing. In Proceedings of International Conference on Computational Science and Applications, Singapore, May 2005.
- X. Jiao and M. T. Heath. Feature detection for surface meshes. In Proceedings of 8th International Conference on Numerical Grid Generation in Computational Field Simulations. Pages 705-714, Honolulu, HI, June, 2002.
Past student:
- Narasimha Bayyana
We develop geometry-aware parallel software framework and high-performance geometric and numerical algorithms. Research activities include hard-ball molecular dynamics, finite-element and boundary-element methods, parallel mesh adaptation.
Selected Publications:
- J.-C. Huang, X. Jiao, et. al., Efficient parallel algorithm for hard-ball interactions. In preparation.
- X. Jiao, G. Zheng, P.A. Alexander, M.T. Campbell, O.S. Lawlor, J. Norris, A. Haselbacher, M.T. Heath, A system integration framework for coupled multiphysics simulations, Engineering with Computers, in press, 2006.
- X. Jiao and P. Alexander, Parallel feature-preserving mesh smoothing. In Proceedings of International Conference on Computational Science and Applications, Singapore, May 2005.
Past students:
- Ankita Jain, Rao Bayanna
Data is ubiquitous in science and engineering. The problems of interests include manifold learning, facial recognition, and extracting computational meshes from medical images.
Past Students:
- Gopal Pai (with Park)
Research supported by the U.S. Department of Energy through the University of California under subcontract B523819 with the University of Illinois at Urbana-Champaign (UIUC), by NSF/DARPA under CARGO grant #0310446, by Boeing through contract with UIUC, and by UIUC under subcontract C65-649 with Georgia Tech. These supports are greatly appreciated.
Last updated on 10/11/2007.
