.. _preliminaryresults:

Preliminary results
--------------------

We performed a set of experiments and we presented them into the
*"Star Clusters and Black Holes in Galaxies Across Cosmic Time"*
(`IAU Symposium #312`_) under the title
**GraviDy, a modular, GPU-based, direct-summation N-BODY integrator**,
*C. Maureira-Fredes & P. Amaro-Seoane*.

.. _`IAU Symposium #312`: http://silkroad.bao.ac.cn/iaus312/

Experiments setup
==================

The computational environment used for the following experiments
was:

 * **CPU**,  Intel(R) Xeon(R) CPU X5650 @ 2.67GHz (24 cores)
 * **GPU**,  Tesla M2050 @ 575 Mhz (448 cores).
 * **RAM**,  24 GB
 * **OS**,   Scientific Linux release 6.4

Results
========

Globular cluster evolution
+++++++++++++++++++++++++++


Lagrange radii of an *N-* body system with 1024 particles,
the lines in the plot shows the radii distribution, using
5%, 10%, 15%, ..., 65% of the total mass.
The core collapse is reached at `T_{\rm cc}\,\approx\,15\,T{\rm rh}_{t=0}`,
with a initial half-mass relaxation time of `T{\rm rh}_{t=0}\,=\,20.24` NBU.


.. image:: ../_static/lagrange_radii_1024_1000t.png
   :scale: 100 %
   :alt: Lagrange radii of an `N-`body system with 1024 particles.
   :align: center

-----

Cumulative energy error up to `t=1` NBU as a function of `\eta`.
All the plots represent Plummer spheres with different amount of particles (N).

.. image:: ../_static/test_energy_eta_N.png
   :scale: 100 %
   :alt: Energy conservation using different values for `eta`
   :align: center

-----

Clock time up to `t=1` NBU as a function of `\eta`.
All the plots represent Plummer spheres with different amount of particles (N).

.. image:: ../_static/test_time_eta_N.png
   :scale: 100 %
   :alt: Clock time as a function of `eta`
   :align: center

-----

Performance
++++++++++++

Clock time of integration from `t=1` to `t = 2` NBU using `\eta = 0.01` and
`\epsilon = 0.0001` using different amount of particles (N).

.. image:: ../_static/test_time-1t-N.png
   :scale: 100 %
   :alt: Clock time as a function of `N`
   :align: center

-----

The following plot shows the acceleration of five different implementations
using parallel computing techniques, compared to the single-thread base
run.

 * **OpenMP**, ...
 * **CPU + GPU**, ...
 * **MPI-1**, ...
 * **MPI-2**, ...
 * **GPU**, ...

.. image:: ../_static/test_gpu-acceleration.png
   :scale: 100 %
   :alt: Speed-up
   :align: center

-----


GPU gravitational interactions performance in GFLOPS for different amount of
particles.
The blue line at the top corresponds to the theoretical peak of the double
precision floating point performance.

.. image:: ../_static/test_gflops.png
   :scale: 100 %
   :alt: GFLOPs
   :align: center