Multi-scale Computational Challenge

1. A New Methodology for Multi-scale Simulation of Plasmas Self-Adaptive SimulationsComputational Group at SciberQuest, Inc.in collaboration with Georgia TechSupported by NSF ITR Grant

3. Multi-scale Computational Challenge • Large disparity in spatial and temporal scales • Encompasses many industries/fields (e.g., magnetospheric physics, fusion, astrophysics, biology, etc.).

4. Ground motion recorded in Scotland for the 2004 Sumatra-Andaman earthquake

5. Disparate Temporal and Spatial Scales

6. Heart is part of a large feedback system whose dynamics are nonlinear and multi-scale: L. Goldberger et al., 2002 Only one heart recording is from a healthy patient, the rest suffer from serious heart conditions

7. Global Hybrid Simulation of Magentosphere

8. 3D Global Hybrid Simulation: Karimabadi et al., 2004

9. Linear Mode Properties • Resistive MHD Alfven: • Hall MHD Whistler (immobile ions): Ion Cyclotron:

10. Timestep Is the Problem • Hybrid Whistler dispersion:

12. Structured Mesh

14. Distribution of Cell Size Normalized to Upstream Cell Size of 1 Ion Inertial Length

15. Variations in dt Dominate over Variations in dx

16. Variations in dt (Reduced Scales)

17. Computational Load

18. Traditional Algorithms

19. What is Needed • Push each particle with its own (time varying) Dt • Update fields locally ONLY when there is a reasonable change • MONITOR and EVOLVE the model by tracking its incremental • behavior rather than blindly time-stepping it with prescribed Dt

20. Time Increment is not a Physical Parameter Traditional (time-driven) method: Solve df/dt = S by choosing Dt New (event-driven) method: Solve df/dt = S by choosing df AND have the algorithm figure out proper Dt

22. Adaptive time refinement needs to be independent of spatial refinement

24. Comparison of Ion Acceleration

25. Distinct and Disconnected Fields of Simulation and Modeling • Time-Stepping (Time-Driven) Simulations: • Heavy emphasis on adaptive mesh and implicit techniques • Used for solving PDEs • Event-Driven Simulations: • Used in operations research, war games, etc. • Have not incorporated spatial mesh techniques • Have only been applied to systems with “small” number of events

26. A New Approach to Time Integration • Time-Stepping Advance: • Depends on adaptive spatial mesh techniques • Event-Driven Advance: • Uses irregularly time-stamped events which only update what needs to be updated when it needs to be updated Use adaptive meshes for refinement in space and event-driven advance for self-adaptive refinement in time

27. Electrostatic Example

31. Stable Even When CFL is Broken CFL Df ~ 0.0003

32. Hybrid Field Update (B-based) • A and E are cell-centered, B is face-centered • Use dB (through ) to get • Use in • Since know E, then integrate A • Use to get new B

33. Hybrid DES Simulation of a Fast Magnetosonic Shock

34. Hybrid - Temporal “Mesh”

35. Parallel Issues PTDS: key metric is scaling with the number of processors PDES: a) Possibility of out of order execution b) Issue of key metric more complex and is related to comparison with serial performance

36. PDES Strategies • Traditional - Conservative – requires lookahead - Optimistic – allow rollback • DES-PIC - Preemptive Event Processing - Out of order Execution

37. DES-PIC Synchronize after some time interval tsynch: 1. Preemptive event processing - use a sliding window to preempt out of order execution - advance in quantized time, all events pulled back to quantized timestamps within the “window” 2. Out of order execution - only occurs at boundaries - question is whether “error” is acceptable

38. Summary • By combining techniques from two distinct fields, more efficient algorithms are obtained with superior performance metrics: - Accuracy - Stability - Speed • Has immediate implications for Vlasov, full particle, and MHD/Hall MHD codes