N-Body refers to a number of bodies such as stars in a galaxy on a very large scale or bio-molecules within a cell on a very small scale.  Scientists have attempted to develop models and make observations of their behaviors and they have not gone far because all bodies interact with each other and the counts of bodies are far beyond our day to day visible scale.  We have to resort to simulations as a method to stimulate our thoughts. 

N-Body Simulations are mathematical models with time dependency.  Properties of bodies change with time.  Change of any properties of any one body would have a direct or indirect effect on all other bodies.  Simulations by computations will reveal patterns of behaviors over time and state of affairs at any one time, and these types of artificial information would provide stimulations and ideas for our inquiries into nature.    

The tests Compucon did and reported here are in the domain of astrophysics with gravity as the main force between stars in a galaxy.  The mathematical model was taken from an open source community and Compucon did not have any inputs to the model.  The purpose of Compucon tests is to find out how well our hardware tools will handle the simulation process. 

All bodies exert a force on other bodies simultaneously.  We can attempt to use the conventional approach of computer simulation by running software codes by hardware processors in series.  This will not be a joyful process as we talk about an astronomical number of processes happening at the same instant and at all instants.  We must resort to parallel processing for this type of simulation.  Tesla from Nvidia was designed and developed squarely for this purpose. 

We were interested in the computational abilities of the hardware and not on the scientific implications of simulations on this occasion.  We show 3 figures of test results below.  In each figure, we show the computational performance for a very small number of bodies (2000) to start with and up to 50K (thousand) which is still a very small number in the cosmos.  Scientists have predicted over 1000B (billion) of stars in the Milky Way Galaxy. 

The test system is a standard Compucon Superhawk Plus with 16GB of main memory and a standard 7200rpm hard disk running Windows 7 Professional 64bit version. Parallel computation capabilities tested were Quadro 2000 (with 448 cores and 1GB memory), Tesla C2075 (with 512 cores and 6GB memory), and 2x Tesla C2075.

(Hover Mouse Over To View Figures)      
# Figure 1: Total time per 10 iterations in ms
# Figure 2: Number of interactions in billion per second
# Figure 3: GFLOPS at 20 FLOPS per interaction on single precision

The figures show that the performance of one Tesla card flatted out at about 50K bodies on 500GFLOPS, and that 2 Tesla cards hit 1TFLOPS at 50K and would go up further beyond 50K.  This implies the needs for a very high level of parallel computation power for scenarios involving a large count of bodies such as galaxies.  Forget Quadro.  Put in more Tesla. 

Nvidia specified C2075 as having 1TFLOPS peak.  1000 Tesla C2075 will give us more than 1PFLOPS by simple arithmetic.  It is not difficult to go past IBM Sequoia which was ranked world #1 in June 2012 with 16PFLOPS.   Cost is 16K x $2K = $32M for an idea.

We repeated the tests with double precision.  As expected, we obtained the same pattern of computational performance as for single precision.  The figures below show SP and DP together.  DP is double of SP in count of decimals, but the performance of Tesla for DP is less than half of SP.

Heterogeneous hardware performance, CUDA specifically, for super-computing purposes will be analysed in a separate article to be published in September 2012 on this website.