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Scalable Numerical Algorithms and Methods on the ASCI Machines

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Title: Scalable Numerical Algorithms and Methods on the ASCI Machines Author: Ewing Lusk Last modified by: Tim Stitt – PowerPoint PPT presentation

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Title: Scalable Numerical Algorithms and Methods on the ASCI Machines


1
CS61V
Overview of High-Performance Computing
Part II
2
Parallel Programming?
ENIAC, University of Pennsylvania
1946 (http//www.library.upenn.edu/special/gallery
/mauchly/jwmintro.html)
3
The Need For Power
4
Computational Science
  • Traditional scientific and engineering paradigm
  • Do theory or paper design
  • Perform experiments or build system
  • Replacing both by numerical experiments
  • Real phenomena are too complicated to model by
    hand
  • Real experiments are
  • too hard, e.g., build large wind tunnels
  • too expensive, e.g., build a throw-away passenger
    jet
  • too slow, e.g., wait for climate or galactic
    evolution
  • too dangerous, e.g., weapons, drug design

5
Computational Science Examples
  • Astrophysical thermonuclear flashes
  • Nuclear weapons
  • Weather prediction
  • Climate and atmospheric modeling
  • Drug design
  • Blood flow
  • Fluid dynamics (CFD)

6
Fluid Dynamics
  • Hairpin vortex generation
  • Forced convective heat transfer
  • Buoyant convection
  • Rayleigh-Taylor instability

7
Hairpin Vortices - Transition to Turbulence
  • Boundary layer flow past a hemispherical
    roughness element
  • Re200-2000 based on hemisphere height
  • K512-8168 spectral elements of polynomial degree
    N7-15

8
Simulation Cost
  • Cost is O(Re3)
  • Re1K simulation 1 week on 512 processors of
    ASCI Red
  • 50GF, 64 GB
  • Re10K 1 year on all 8192 processors of ASCI
    Red
  • 800GF, 1TB
  • Were really interested in Re1M
  • Cant even think of doing the Re1K problem on a
    uniprocessor machine let alone the 10K or 1M
    problems!

9
The Necessity of Parallel Computing
10
How fast can a serial computer be?
1 Tflop 1 TB sequential machine
r .3 mm
  • Consider the 1 Tflop sequential machine
  • data must travel some distance, r, to get from
    memory to CPU
  • to get 1 data element per cycle, this means 1012
    times per second at the speed of light, c 3e8
    m/s
  • r lt c/1012 0.3 mm
  • Now put 1 TB of storage in a .3 mm2 area
  • each word occupies about 3 Angstroms2, the size
    of a small atom

11
Even if we could make it ...
  • ... itd be too expensive
  • Market forces are dictating use of COTS

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The Solution ?
  • Add more workers!
  • Use a collection of processors and memory
    modules to work together to solve our problems
  • Supercomputers, MPPs, Clusters, Beowulfs

20
Bad News
21
Still Lots of Work
  • Decide on and implement an interconnection
    network for the processors and memory modules
  • Design and implement system software for the
    hardware
  • Devise algorithms and data structures for solving
    our problems
  • Divide the algorithms and data structures up into
    subproblems
  • Identify the communication that will be needed
    between the subproblems
  • Assign subproblems to processors and memory
    modules

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Modern Layered Framework
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