High Performance Computing: A Historical Perspective and Modern Trends - Prof. John Wallin, Study notes of Computer Science

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CSI 702

High Performance Computing

Dr. John Wallin

Research I, room 352

703-993-

[email protected]

http://www.cos.gmu.edu/

jwallin/c702f

1

• My Interests (^) observations and simulations of colliding galaxies

(^) numerical methods

(^) high velocity impacts

(^) high performance computing

A Mini-Quiz

3. How do you use tar and gzip to compress and backup a direc-2. How do you delete, rename, or move a file? 1. How do you create, change, or move directories? tory?
4. What file and directory permissions are required to set up a website on your account?
5. How do you find the location of a binary that you wish to6. How do you modify your path?5. In which directory do you normally place your web-pages? execute?

8. Have you Used Matlab to simulate real-world problems, such as a traveling salesman problem?
9. Have you ever used regular expressions to do searches?

Why Do Scientist Use Computers

(^) experiments are impossible

(^) experments are too expensive

(^) equations too difficult to be solved analytically

(^) experiments don’t provide enough insight or accuracy

(^) data sets too complex to be analyzed by hand

Computers bridge the gap between experiments and theory

What is a supercomputer?

why we need them. Define what a supercomputer is and come up with some reasons

Supercomputer Speeds

(Taken from

http://home.earthlink.net/ mrob/pub/computer-history.html

and http://www.top500.org/main/archive.php)

Year

Computer

speed

CPU

Eniac

500 FLOPS

IBM 704

10 kFLOPS

CDC 6600

1.2 MFLOPS

Cray 1

12.5 MFLOPS

Cray Y-MP

2 GFLOPS

Fujitsu Numerical Wind Tunnel

124.5 GFLOP

ASCI Red (Sandia)

2.4 TFLOP

2005 BlueGene/L (DOE/NNSA/LLNL)

280 TFLOP

10

Supercomputer Speeds - new additions

Year

Computer

speed

CPU

Eniac

500 FLOPS

IBM 704

10 kFLOPS

CDC 6600

1.2 MFLOPS

Cray 1

12.5 MFLOPS

Cray Y-MP

2 GFLOPS

Fujitsu Numerical Wind Tunnel

124.5 GFLOP

ASCI Red (Sandia)

2.4 TFLOP

2005 BlueGene/L (DOE/NNSA/LLNL)

280 TFLOP

Dual Core AMD/Intel

30-50 GFLOPS

NVIDIA 8800 GTX Video Card

350-500 GFLOPS

11

Historical Trends in SuperComputing (2) 100 1000

10000100000 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12 1e+ 1940

1950

1960

1970

1980

1990

2000

FLOPS/CPU

year

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The Drive toward High Performance Computing

(^) resolution

(^) dimensions

(^) physical realism

The Euler Equations

by the Courant condition Consider the Euler equations. The size of the time step is limited

δt (^) =

δx

min(

v i, c i)

where

(^) δx (^) is the grid size,

(^) v i is the bulk fluid velocity, and

(^) c i is the

If we double the resolution, we decreaselocal sound speed.

(^) δx (^) by a factor of two AND

physical problem with twice the spatial resolution.This means we need four times the CPU time to to solve the samehalf the size of the time-step.

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N-body Methods

order of calculations goes ascles. Since every particle exerts a force on every other particle, the The first N-body simulations included only a few hundred parti-

O

(n ).^2

stars.The current state of the art cosmological simulation has 10 billionto simulate the volume that contains 10,000 or more galaxies.dark matter and gas. Modern cosmological simulations usually tryThere are about 100 billion stars in our galaxy, not including the

17

Physical Realism

Similar problems occur across Computational Science.structure of the galaxyphysical effects by their relative importance in changing the overallIf you take the example of galaxies, we can characterize differentany particular simulations.ever, there are always choices in how much physics to include in Any set of equations is an approximation to physical reality. How-

Galaxy Dynamics

Observation vs Simulation