Transcript Time-stepped - SciberQuest

A New Approach to Modeling of
Physical Systems
Distinct and Disconnected Fields
of Simulations and Modeling
Time-stepped:
• Heavy emphasis on spatial grid techniques
• Used for solving PDEs
• Outdated time advance schemes
Event-stepped:
• Used in operations research, war games, etc.
• Has not incorporated spatial grid techniques
• Has only been applied to systems with “small” number of events
A Simple Test Problem
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Start with an initial
distribution of “entities”
The speed of each entity
is a function of the total
number of entities in
each “bin”
New entities are
periodically “injected”
into the simulation zone
Time-stepped Algorithm:
Courant Condition: Dt = fastest speed/bin width
Standard Recipe
1. Pick one physics model
2. Use space and time differencing of the eqns
a. introduce spatial grid
 2  
d 2 / dx2 | 
i
2[(  ) /    (  ) /   ]/(    )  
i i1
i
i1 i
b. Advance the equations based on a uniform time step
Problems With Time-stepped
Algorithm
• Tracks movement of each entity at the same
time resolution Dt, independent of its speed.
• Recalculates the entity’s speed regardless of
whether the number of entities in a given bin
has changed.
• Lots of computations even if there is no
“congestion.”
Alternative: Event Based Modeling
Current Computational Demands
 Multi-scale Coupled Systems
- Spatial scales vary from centimeters to 200 RE
- Temporal scales vary from less than milliseconds to
days
- Kinetic effects have large-scale consequences
 Multi-physics
- electron physics: e.g., controls reconnection
- ion physics: e.g., dominates formation of boundaries and transport
- global features and dynamics: e.g., extent of the magnetotail
- coupling to the ionosphere
Structured Mesh
Why Is the Current State-of-theart Not Adequate?
1. Time advance scheme is too inefficient
- Every cell is updated regardless of whether a
change has occurred
- Time step is not based on local conditions
2. Existing time advance schemes do not
allow code-code coupling
3. The “curse” of Courant condition
- physically the system should be stable if there is
no change regardless of how fast information is
propagating but numerically it is not
Simulation Model
Resolution
Memory Requirement
(Bytes)
Run Time / 1 hour of
Magnetosphere
Time*
Full Particle (mi/me=200)
Electron Scales
1017
1.2x107 Years
Hybrid**
Ion Scales
3x1011
2 Months
A New Approach
Time-stepped:
Sophisticated spatial mesh techniques
Event-stepped:
Uses irregularly time-stamped events that
only updates what needs to be updated
when it needs to be updated
Combine the spatial mesh techniques of
time-stepped with time advance method of
event-stepped
Test Example: I
Test Example II
Summary
• By combining techniques from two
distinct fields, more efficient
algorithms are obtained
• Application to plasmas demonstrate
speed up of over a factor of 100 in
1D, with projected speed of 105 in
3D
• General enough to be applicable to
other areas where time-stepped
methodology are in use