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Duane Rosenberg , Aimé Fournier, Paul Fischer, Annick Pouquet

Dynamically adaptive geophysical fluid dynamics simulation using GASpAR: Geophysics/Astrophysics Spectral-element Adaptive Refinement. Duane Rosenberg , Aimé Fournier, Paul Fischer, Annick Pouquet. NCAR Institute for Mathematics Applied to Geosciences Turbulence Numerics Team.

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Duane Rosenberg , Aimé Fournier, Paul Fischer, Annick Pouquet

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  1. Dynamically adaptive geophysical fluid dynamics simulation using GASpAR: Geophysics/Astrophysics Spectral-element Adaptive Refinement Duane Rosenberg, Aimé Fournier, Paul Fischer, Annick Pouquet NCAR Institute for Mathematics Applied to Geosciences Turbulence Numerics Team

  2. Motivation: Methodology Requirements Variable (e.g., high) order method (Patera 1984) Must be non-dissipative for DNS Must also model small scales, high Re, complex boundaries Must support variety of equations, physical models, geometries  code extensibility Leverage existing NCAR expertise in science applications, methods and performance

  3. GASpAR Features • Designed for turbulence studies • Object oriented (C++) • extensive use of inheritance, polymorphism, templates • Hierarchical: Elements  Fields  Eq. solvers SEM operators  Bases  GBLAS • Adaptive Mesh (currently 2D unstructured) • Parallelized

  4. Spectral element numerics • Based on spectral-element operators • Typically, use operator-vector products • basic matrix-matrix products (m_x_m)

  5. Handling Nonconformity SCD User Forum 2005

  6. Connectivity uses “mortars” (color matched)

  7. Locating neighbors and constructing mortars: VDB (Henderson 1993)

  8. ‘Mortar’ Data Exchange • Mortar nodes given unique Morton keys (Warren & Salmon 1993) • Bin-sort keys and create node/processor map • Do DSS

  9. Adaptation Rules • Isotropic (for now) • Refinement: • At most 2 child edges (4 child faces in 3D) • Edge bisection • h-refinement only (currently) • Max. number of refinement levels • Coarsening: • Cannot coarsen root • All siblings must be tagged • Must not violate Refinement rules

  10. Refinement & Coarsening Criteria • a-posteriori spectral estimator of Mavriplis (1990) • gradient2 magnitude • open question for turbulent flows (esp. in various formulations of the equations)

  11. Development/Porting Strategy • Initial development under Linux using gcc • Test MPI using MPICH with 1 or 2 procs • Locate bottlenecks with port to Lightning (use PG compilers with -Minfo=loop,inline) --Find C m_x_m will not vectorize, but Fortran will! --Factor of 10 speedup in m_x_m! • Port to IBM SPs (VAC++, f77) --Use gprof, HPM --Debug with totalview and printf’s

  12. Advecting Gaussian ‘Lump’

  13. Advecting Gaussian ‘Lump’ Mesh

  14. Radial N-wave Solution for Nonlinear Burgers Eqn.

  15. Rotated Burgers Front

  16. Dynamical Systems: Large Scale Passive Advection of Small Scale Field

  17. Conclusion 2D adaptive algorithm is working Must include dynamic load balancing/processor distribution. Complete 3D AMR, enhance performance based on 2D; debugging difficult Better performance monitoring/reporting on the SPs?

  18. Nonconforming Connectivity: non-Boolean gather operator Q maps global (j=0:18) to local (i=0:26) d.o.f.(after Fischer & Kruse 1997) Qi,j Q12,2

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