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 - PowerPoint PPT Presentation

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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

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Title: 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


1
A New Paradigm for Time Integration of
Multi-Scale SystemsSelf-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 Earths
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/dtS solve dt/df1/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)
  • Generic framework (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 (Dconst, )

15
Nonlinear Diffusion ( )
16
Diffusion-Convection
17
PIC-DES Simulation
  • Particles are pushed with individual (time
    varying) Dts
  • 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
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20
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

21
Weak Fast Shock (M2, )
22
Rotational Discontinuity (M0, )
23
Intermediate Shock (M1.05, )
24
Strong Fast Shock (M6, )
25
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26
Parallel Issues
PTDS key metric is scaling with the number of
processors (performance) PDES issue of key
metric more complex (resolution performance)
27
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)

28
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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