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
1A 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
2Multi-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.)
33D Global Hybrid-PIC Simulation of Earths
Magnetosphere Karimabadi et al., 2004
4Computational Load
5What 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
6Self-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)
7Discrete Event Simulation (DES)
8Event Processing
Advance update solution
Synchronize propagate
change Schedule predict new update
9Convection-Diffusion-Reaction
10What About Flux Conservation?
- It is what makes time travel possible the
flux capacitor. - Dr. Brown, Back to the
Future.
11Flux Synchronization
12Linear Diffusion-Reaction
13Linear Advection
14 Heat Wave (Dconst, )
15Nonlinear Diffusion ( )
16Diffusion-Convection
17PIC-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
18PIC-Field Synchronization
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20Hybrid-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
21Weak Fast Shock (M2, )
22Rotational Discontinuity (M0, )
23Intermediate Shock (M1.05, )
24Strong Fast Shock (M6, )
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26Parallel Issues
PTDS key metric is scaling with the number of
processors (performance) PDES issue of key
metric more complex (resolution performance)
27Preemptive 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)
28Summary
- 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