1. AstroBEAR Finite volume hyperbolic PDE solver Discretizes and solves equations of the form Solves hydrodynamic and MHD equations Written in Fortran, with MPI support libraries

2. Adaptive Mesh Refinement Method of reducing computation in finite volume calculations Starts with a base resolution and overlays grids of greater refinement where higher resolution is needed. Grids must be properly nested For parallelization purposes, only one parent per grid

3. AMR Algorithm (Cunningham et al., 2009)‏ AMR(level, dt) { if (level == 0) nsteps = 1; if (level > 0) nsteps = refine_ratio; For n = 1, nsteps { DistributeGrids(level); IF (level < MaxLevel) { CreateRefinedGrids(level + 1); SwapGhostData(level + 1); } Integrate(level, n); If (level < MaxLevel) CALL AMR(level + 1, dt/refine_ratio); } If (level > 1) synchronize_data_to_parent(level); }

4. Parallel Communications Grids rely on external “ghost cells” to perform calculations. Data from neighboring grids needs to be copied into ghost region. Major source of scaling problems Alternate fixed-grid code (AstroCUB) has different communication method

5. AstroBEAR Parallel Communication TransferOverlapData() { TransferWorkerToWorkerOverlaps(); TransferMasterToWorkerOverlaps(); TransferWorkerToMasterOverlaps(); } foreach overlap transfer t { If (Worker(t.source)) SignalSendingProcessor(t.source); If (Worker(t.dest)) SignalReceivingProcessor(t.dest); IF (Worker(t.source)) SendLocalOverlapRegion(t.source); IF (Worker(t.dest)) SendLocalOverlapRegion(t.dest); }

6. AstroCUB Parallel Communication TransferOverlapData(Grid g) { for dim = 1, ndim { foreach boundary along dim { foreach field_type { MPI_ISEND( at ); MPI_IRECV( at ); MPI_WAIT(); }

7. AstroBEAR/AstroCub Comparison AstroBEAR:  Recalculates overlaps before each synchronization  Each send/receive operation is handled individually  Groups transfers based on source and destination processor (master or worker)‏  10 MPI calls per grid per timestep in 3D hydro runs AstroCUB:  Calculates overlaps once, prior to first synchronization  Send/receive operations handled together  6 MPI calls per processor per timestep in 3D hydro runs

8. Requirements Physics  Hydro/MHD  Cooling  Cylindrical Source  Self-Gravity  Sink Particles Numerics  MUSCL-Hancock, Runge-Kutta  Strang Splitting  Constrained Transport  Roe, Marquina Flux

9. Language Options Python:  Pros: Good stack trace, flexibility, resource management  Cons: Requires SciPy, GPU or hybridization for numerics C:  Pros: Speed, no interfaces required  Cons: More memory, pointer management work falls on developer Fortran:  Pros: Fast number-crunching  Cons: Clumsy data structures, more memory and pointer management for developer

10. Hybridization Not unheard-of in scientific codes  Cactus (Max Planck Institute)‏ We've tried it already (HYPRE)‏ Can benefit from strengths of scripting and compiled languages May result in steeper learning curve for new developers

11. Parallelization Improvements Transmission caching  Each processor stores its ghost zone transmission details until regrid Message packing  Sending big blocks containing many messages msg 1 msg2msg3

12. Parallelization Improvements, ctd.  Redundancy in root domains “Stretching” root grids initially to pull in extra data from other grids Reduces the need for refined ghost transmissions core grid stretched grid

13. Further Options for Improvement Refined grids: Can Berger-Rigoutsos be further simplified/parallelized?

14. Concerns for New Code Solver Modularity  Code should run on CPU cluster or GPU cluster Scalability  Code must run effectively on more than 64 CPUs