Teaching
Research
My research interests are in applied and computational mathematics, numerical analysis and PDEs for scientific computation. In particular, I study adaptive finite volume methods for hyperbolic conservation laws and related problems. I work with applications in geophysics and biophysics. I am working with Randy LeVeque and graduate students Kyle Mandli, Kirsten Fagnan and David Ketcheson.
Research Projects
Some specific research projects and interests are below.
- The Geoclaw software project. Adaptive finite volume methods for geophysical flows and wave propagation.
- Tsunami modeling using adaptive finite volume methods.
- Dam break and flood modeling with finite volume shock-capturing methods.
- Debris flow modeling using shallow-water and depth averaged equations with stress terms.
- Inclusion of vertical (gravity-correction) terms into the shallow water equations.
- A study of rip currents using shallow water equations vs. KP equations.
- Modeling of biological fluid dynamics and biophysics with complex geometries (interfaces).
Software
- GeoClaw is becoming a subset of the Clawpack software, specifically for geophysical flow problems. The official website is http://www.geoclaw.org . You can download the tar-zipped code below and documentation for GeoClaw. Note that this is a stripped-down version of what will eventually become the next version of Clawpack. The code below includes everything necessary to run GeoClaw and nothing more. Eventually, the released versions of Clawpack will include all of the functionality of the code below, as well as additional functionality for other hyperbolic problems. For usage restrictions see the official Clawpack website.
- Download Code: geoclaw_v4.4.tar.gz (version 4.4 - March 2008)
- Download Documentation: GeoClawDoc.pdf
- Download Topography ( topo.tar.gz ) to run the example Indian Ocean tsunami, in geoclaw/applications/sumatra26dec04/BengalBay.
Publications
- Adaptive Mesh Refinement Techniques for Geophysical Flows and Waves over Topography. M. J. Berger, D. L. George and R. J. LeVeque. In preparation, 2008.
- Augmented Riemann Solvers for the Shallow Water Equations over Variable Topography with Steady States and Inundation. D. L. George. J. Comp. Phys. , 227(6):3089-3113, 2008. Info/Download .
- High Resolution Methods and Adaptive Refinement for Tsunami Propagation and Inundation. D. L. George and R. J. LeVeque. Hyperbolic Problems: Theory, Numerics, Applications., pages 541-549. Springer, 2008. Proc. 11'th Intl. Conf. on Hyperbolic Problems, HYP06, Lyon, France, July 2006. (refereed proceedings.) Info/Download .
- High-Resolution Finite Volume Methods for the Shallow Water Equations with Bathymetry and Dry-States. R.J. LeVeque and D.L. George. In volume 10 in Advanced Numerical Models for Simulating Tsunami Waves and Runup, P. L. Liu, C. Synolakis, and H. Yeh, editors., Advances in Coastal and Ocean Engineering, , pages 43-73. World Scientific 2008. Info/Download .
- Finite Volume Methods and Adaptive Refinement for Global Tsunami Propagation and Indundation. D.L. George and R.J. LeVeque. Science of Tsunami Hazards, Vol. 24. No. 5, 319-328, 2006. pdf .
- Finite Volume Methods and Adaptive Refinement for Tsunami Propagation and Inundation. Ph.D. Thesis, Department of Applied Mathematics, University of Washington, Seattle, 2006. pdf .
Talks
- AGU Fall Annual Meeting, San Francisco, CA, December 2007. U51A-0014: ``Modeling Indian Ocean Tsunami Propagation and Inundation with TsunamiClaw---Adaptive Finite Volume Methods.''
- SIAM Conference on Mathematical and Computational Issues in the Geosciences, Santa Fe, NM, March 2007. Contributed Talk: ``Wave Propagation Algorithms and Adaptive Refinement for Tsunami Modeling.'' Session Chair: ``Ocean Modeling."
- SIAM Conference on Computational Science and Engineering, Costa Mesa, CA, February 2007. Special Session on Wave Propagation Algorithms. Invited Talk: ``Adaptive Refinement for Tsunami Modeling.''
- Eleventh International Conference on Hyperbolic Problems, Theory, Numerics, Applications. Ecole Normale Superieure de Lyon, Lyon, France, July 2006. ``High-Resolution Methods and Adaptive Refinement for Tsunami Propagation and Inundation.''
- The Third Tsunami Symposium of the Tsunami Society. University of Hawaii, Honolulu, May 2006. ``Finite-Volume Methods and Adaptive Refinement for Global Propagation and Local Inundation.''
- Simon Frasier University, Department of Mathematics and Statistics. Vancouver, BC, January 2006. ``Finite Volume Methods and Adaptive Mesh Refinement for Tsunami Modeling.''
- Harvey Mudd College Mathematics Conference on Scientific Computing. Claremont, California, November 2005. Poster Presentation: ``Adaptive Mesh Refinement for Tsunami Modeling.''
- Pacific Northwest Numerical Analysis Annual Seminar (PNWNAS). Western Washington University, October 2005. ``Tsunami Modeling.''
- SIAM Annual Meeting. New Orleans, July 2005. ``Finite Volume methods for Tsunami Modeling,'' R. J. LeVeque and D. L. George.
- NSF Workshop on Tsunami Deposits and Their Role in Hazard Mitigation. University of Washington, June 2005. Poster Presentation: ``Adaptive Mesh Refinement for Numerical Tsunami Modeling.''
- University of Victoria, Department of Mathematics and Statistics. Victoria, BC, November 2004. ``A Wave-Propagation Method for the Shallow Water Equations.''
- SIAM Annual Meeting. Portland, OR, July 2004. ``A High-Resolution Method for the Shallow Water Equations: Capturing Moving Shorelines over Topography.''
- Workshop on Free Surface Water Waves. The Fields Institute for Mathematical Research, Toronto, June 2004. Poster Presentation: ``A High-Resolution Godunov Method for the Shallow Water Equations with Topography and Evolving Dry Regions.''
·Curriculum Vitae ·
|
![[Hi]](pictures/france0706 003.jpg)