Transcript Computational Math Group Amik St-Cyr, Ram Nair, Natasha Flyer Group Head: Piotr Smolarkiewicz.

Computational Math Group
Amik St-Cyr, Ram Nair, Natasha Flyer
Group Head: Piotr Smolarkiewicz
Group Goals and Research
Goals:
• Develop novel numerical methodologies for the geosciences
• Bridge communities of applied/numerical math with geoscience
Background of the Group:
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Applied mathematics
Computational mathematics
Geophysical fluid dynamics
Numerical weather predication
Examples of our research:
• High-Order Method Modeling Environment (HOMME)
• Non-conforming spectral element model
• Radial Basis Functions (Meshless method)
Hydrostatic Dynamical Core (HOMME)
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Discontinuous Galerkin based new generation dynamical core development
in HOMME framework (High-Order Method Modeling Environment)
Inherently conservative, Geometric flexibility and highly scalable
[Simulated temperature field for the J-W baroclinic instability test at a resolution 0.7 degree with DG/HOMME]
Ongoing Research: Extend HOMME further to a full-fledge conservative
dynamical core by incorporating NCAR-CAM physics packages.
Barotropic Vorticity Evolution
Non-conforming spectral element model on the sphere
0.3125 degrees...
RBFs: Moving Vortices on a Sphere
(Flyer and Lehto ’09, Nair and Jablonowski ‘08)
Moving vortices on a sphere (RBFs)
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12 Days Simulation, N = 3136, Time-Step= 20 minutes (RK4)
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Collaborations
NCAR: CGD, HAO, MMM
National:
Courant Institute, Oakridge National Labs, Sandia National
Labs, NCEP, Temple University, Columbia University,
University of Michigan, University of Colorado-Boulder,
University of Wyoming, North Carolina State, University of
Minnesota, Florida State University, University of CaliforniaDavis, Boise State University, Arizona State University,
Wichita State University
International:
Chinese Academy of Science, UK Met office, University of
Copenhagen (DK), Uppsala University (S), University of
Cambridge (UK), University of Oxford (UK), Kyungpook
National University (Korea), University of Stellenbosch
(South Africa), University of Victoria (Canada), University of
Geneva (CH), Universite Louvain la Neuve (B)
Community Interaction
Organized Workshops/Mini-symposiums
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European Conference on Numerical Mathematics (ENUMATH)
PDEs on the Sphere
Korea SIAM Annual Meeting
SIAM Computational Issues in the Geosciences
SIAM Annual meeting
SIAM Parallel processing
SIAM Computational Science and Engineering
International Conference on Computational Science
International Conference on Spectral and High Order Methods
International Conference on Domain Decomposition Methods
Copper Mountain Conference on Iterative Methods
NCAR ASP Summer Colloquium 2008
Student/Post-doctoral Mentoring-Support
University of Oklahoma, University of Colorado, University of
Minnesota, North Carolina State, University of Michigan,
University of Wyoming, Indian Institute of Science (IISc) Bangalore,
Indian Institute of Technology (IIT) Madras, University of Toronto,
Uppsala University (Sweden)
Geophysical Modeling Motivations for Research
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Modeling coupling
Necessary scalability
Non-hydrostatic dynamics for realism
Free-boundary problems
Geometric flexibility
Algorithmic simplicity
Realistic time-stepping
Bottom Line
High-resolution and numerical accuracy at low computational
costs to resolve the multi-scale features of the earth system
Meeting the Computational Challenges
Advancing the frontier:
• High-order accurate methods
– Meshless methods
– Finite volume methods
– Continuous and discontinuous Galerkin methods
• Scalable Numerics:
– Conservative re-mapping of arbitrary grids
– Optimized Schwarz solvers
– Time-integrators (Lagrangian, Eulerian)
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Conservative non-oscillatory transport schemes
Adaptive mesh-refinement with error estimation
Unstructured meshes
Peta-Scale capable algorithms
Thank You