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Multi-Scale Challenge

A New Paradigm for Time Integration of Multi-Scale Systems: Self-Adaptive Event-Driven Simulation Computational Group at SciberQuest, Inc. Solana Beach, CA in collaboration with Georgia Tech. Multi-Scale Challenge. Large disparity in spatial and temporal scales due to system inhomogeneity

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Multi-Scale Challenge

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  1. A New Paradigm for Time Integration of Multi-Scale Systems:Self-Adaptive Event-Driven SimulationComputational Group at SciberQuest, Inc. Solana Beach, CA in collaboration with Georgia Tech

  2. Multi-Scale Challenge • Large disparity in spatial and temporal scales due to system inhomogeneity • Encompasses many scientific fields (e.g., space physics, fusion, climate modeling, biology, materials science, etc.)

  3. 3D Global Hybrid-PIC Simulation of Earth’s Magnetosphere: Karimabadi et al., 2004

  4. Computational Load

  5. What is Wrong with Time Stepping? • DEGENERACY: • Idle Systems: • Stiff Systems GOAL: Update micro-states (particles, fields etc.) with rates determined by local physical time scales • SOLUTION: • For df/dt=S solve dt/df=1/S by predicting Dt based on rate of change, df/dt and threshold (quantum) value, Df • Monitor and correct solution behavior via causal (not parametric) time dependencies

  6. Self-Adaptive DES • Fast (no redundant computation) • Accurate (validated against TDS) • Stable (even in super-Courant regimes) • Multi-D (extendable) • Parallel (MPI) • Genericframework (PDE,PIC) • Ideal for nonuniform meshes (AMR, unstructured, mapped)

  7. Discrete Event Simulation (DES)

  8. Event Processing Advance: update solution Synchronize: propagate change Schedule: predict new update

  9. Convection-Diffusion-Reaction

  10. What About Flux Conservation? “It is what makes time travel possible – the flux capacitor.” - Dr. Brown, “Back to the Future”.

  11. Flux Synchronization

  12. Linear Diffusion-Reaction

  13. Linear Advection

  14. Heat Wave(D=const, )

  15. Nonlinear Diffusion ( )

  16. Diffusion-Convection

  17. PIC-DES Simulation • Particles are pushed with individual (time varying) Dt’s • Fields are updated with rates proportional to local frequencies • PIC and field micro-states are synchronized via “wake-up” calls

  18. PIC-Field Synchronization

  19. Hybrid-DES Model • A and E are cell-centered, B is face-centered • Use (through ) to predict • Get A-quantum, • Integrate A asynchronously (through ) • Get • Push particles with

  20. Weak Fast Shock (M=2, )

  21. Rotational Discontinuity (M=0, )

  22. Intermediate Shock (M=1.05, )

  23. Strong Fast Shock (M=6, )

  24. Parallel Issues PTDS: key metric is scaling with the number of processors (performance) PDES: issue of key metric more complex (resolution + performance)

  25. Preemptive Event Processing (PEP) • Generic approach to parallelization of physics-based DES codes • Event pipeline minimizes inter-processor communication • Ideal for high-resolution computing • Load balancing is based on Event Distribution Function (EDF)

  26. Summary • Elimination of time degeneracy leads to novel, event-driven algorithms with superior performance metrics: - Accuracy - Stability - Speed • Applicable to full-PIC, CFD/MHD and Vlasov simulation models • Ideal in combination with nonuniform meshes

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