CSI 702
High Performance Computing
Dr. John Wallin
ST I, Room 109
703-993-3617
jwallin@gmu.edu
http://www.scs.gmu.edu/∼jwallin/c702s06
Dr. Brett Berlin
1
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High Performance Computing: CSI 702 Course with Dr. John Wallin and Dr. Brett Berlin - Pro, Study notes of Computer Science
Information about the csi 702 high performance computing course offered by george mason university. The course is taught by dr. John wallin and dr. Brett berlin and covers topics such as observations and simulations of colliding galaxies, numerical methods, high velocity impacts, and high performance computing. Prerequisites include fluency with one of the listed computer languages and the unix operating system, as well as csi 700 and csi 701 or instructor permission. Students are expected to use c, c++, fortran 90, or fortran and know how to use matlab and basic numerical methods. The course uses steve mcconnell’s code complete and heath’s scientific computing: an introductory survey textbooks.
Typology: Study notes
Pre 2010
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CSI 702
High Performance Computing
ST I, Room 109Dr. John Wallin 703-993-
http://www.scs.gmu.edu/
jwallin/c702s
Dr. Brett Berlin
1
My Interests
(^) observations and simulations of colliding galaxies
(^) numerical methods
(^) high velocity impacts
(^) high performance computing
A Mini-Quiz
- 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?
- What file and directory permissions are required to set up a website on your account?
- 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?
- Have you Used Matlab to simulate real-world problems, such as a traveling salesman problem?
- 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
The Atanasoff- Berry Computer
of matrix problem is extremely difficult without a computer.Although this seems like a trivial problem now, solving this typebase-2) of modern machines.to a single task, it contained all the elements (storage, digital logic,element linear equation. Even though its programming was limitedIt was a special purpose machine that was used to solve a 27x27and Berry in 1937- 1942.of the Physics Department at Iowa State University by Atanasoff The earliest electronic digital computer was built in the basement
Historical Trends in SuperComputing (1) 100
10000 1e+06^ 1e+08^ 1e+10^ 1e+12^ 1e+14^ 1e+ 1940
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FLOPS
year
10
Historical Trends in SuperComputing (2)
100 1000
10000100000 1e+06 1e+07 1e+08 1e+09 1e+10 1e+11 1e+12 1e+ 1940
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FLOPS/CPU
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Resolution
increase with the number of computational cells.The increase in CPU time is usually much worse than a linearcomputational time increases as well. When we increase the resolution we are using to solve a problem,
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.
14
Dimensions
Early models were typically done in only one dimension.cost of solving physical problems. Adding a physical dimension to a simulation greatly increases the
Most
physical resolution changes the cost fromEven going from a two to three dimensional problem with the samesimulations.is still computationally very expensive to do three dimensionalphysical models are now done easily in two dimensions, but it
O
(n 2 ) to
(^) O (n 3 ) where
n (^) is the grid size along one spatial dimension.
16
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
(^) large scale gravitational encounters
(^) internal gravitational forces
(^) gas dynamics
(^) formation of stars from gas
(^) feedback from star formation back into the gas
(^) active galactic nuclei
model, the closer the results are to the real world.All programs approximate reality, but the better the physical
Are Algorithms Important?
Which is more important:
(^) An efficient Algorithm
(^) A fast computer