Computational Math Group

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Computational Math Group

• Amik St-Cyr, Ram Nair, Natasha Flyer
• Group Head Piotr Smolarkiewicz

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Group Goals and Research

• Goals
• Develop novel numerical methodologies for the
  geosciences
• Bridge communities of applied/numerical math with
  geoscience
• Background of the Group
• 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)

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Hydrostatic Dynamical Core (HOMME)

• 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.
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Barotropic Vorticity EvolutionNon-conforming
spectral element model on the sphere
0.3125 degrees...
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RBFs Moving Vortices on a Sphere (Flyer and
Lehto 09, Nair and Jablonowski 08)
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Moving vortices on a sphere (RBFs)
Longitude
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 California-Davis, 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)

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Community Interaction

• Organized Workshops/Mini-symposiums
• 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)

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Geophysical Modeling Motivations for Research

• Examples
• 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

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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)
• Conservative non-oscillatory transport schemes
• Adaptive mesh-refinement with error estimation
• Unstructured meshes
• Peta-Scale capable algorithms

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• Thank You