download report - Sapienza

Scientific Report 2007-2009
Astronomy & Astrophysics
A2. Evolution of stellar systems and galactic nuclei formation and
activity
Modern theoretical Astrophysics relies crucially on numerical
methods. Actually, the strongly non-linear, out
of equilibrium , physical stages that characterize the environment
of galaxy and star formation, as well as the
dynamics of star clusters in an external field are too
complicated to be faced with analytic approximations.
Gravity is the main engine of all the evolutionary astrophyical
pass, and it is difficult to be taken properly into
account without an overload of computational charge.
Consequently, it is compulsory the use of efficient algorithms
running on supercomputers. Our smal theoretical
astrophysics group has been active since many
years in the field of the study of the evolution of globular
clusters in galaxies, and found that these stellar systems
may be responsible for the structure and activity
of the innermost galactic regions (see [1],[2]). To study
at best the possibility that orbitally decaying massive
stellar clusters form a super-star cluster in the central
region of a galaxy, it is necessary to follow their motion
in the potential of the parent galay, and to study the
mutual galaxy-cluster feedback. This is possible only
by mean of the integration of the complete N-body system
equations. We approach this task in two ways: i)
making use of the CINECA supercomputing facilities,
running our own Tree-algorithm parallelized by mean of
OpenMP and MPI libraries [1], and, ii) with our own
hardware platform, based on 2 Graphic Processing Units
(GPUs) used as supercomputers. Actually, a modern,
cheap approach to supercomputing is through the use of
‘hybrid’ computational platforms, composed by a reliable
multiprocessor host linked with an efficient ‘number
cruncher’, like a GPU board. The structure of this computational
platform is shown in Fig. 1. An optimal
use of this platform required the implementation of a
composite program, called NBSymple as ackronym for
‘N Body Symplectic’ (code), which exploits, thanks to
OpenMP instructions, the power of multicore Intel CPUs
and, thanks to the NVIDIA Computer Unified Architecture
language, the high computational speed of the 240
threads of the individual TESLA C1060 GPU. The time
integration is symplectic, i.e. time-reversible and avoiding
secular term in the energy conservation error. The
description of the code as well as its performances as
computational speed and precision is found in [2]. Fig.
2 is a summary of the code performances of the NBSymple
code in its various versions. The NBSymple code has
presently 5 versions, each labeled with an alphabetic letter
from A to E: NBSympleA is the, basic, fully serial
code running on a single Quad core processor, while NB-
SympleE is the most performant version, uses CUDA on
one or two GPUs to evaluate the total force over the
system stars, i.e. both the all-pairs component and that
due to the Galaxy, while the time integration is done by
the OpenMP part of the code.
Figure 1: The scheme of the HW platform we installed to
perform HP N-body simulations ([3]).
Figure 2: From [3]: the (averaged) solar time (in seconds)
spent for one leap-frog integration step in single precision
mode, as a function of N. Line with empty squares: NB-
SympleA code. Line with filled triangles: NBSympleB. Line
with crosses: NBSympleC. Line with filled squares: NBSympleD.
Line with stars: NBSympleE with a single GPU. Line
with empty triangles: NBSympleE with two GPUs.
References
1. R. Capuzzo-Dolcetta, et al., Mon. Not. of the Roy. Astr.
Soc. 388, Issue 1, L69-L73 (2008)
2. R. Capuzzo-Dolcetta, et al., Astron. Astrophys. 507,
183-193 (2009)
3. R. Capuzzo-Dolcetta, et al., ApJ, 681, 1136-1147 (2008).
4. R. Capuzzo-Dolcetta, Nuovo Cimento 32, 33-36 (2009).
Authors
R. Capuzzo-Dolcetta, A. Mastrobuono-Battisti, M. Montuori
3
http://astrowww.phys.uniroma1.it/astro/dolcetta.html
Sapienza Università di Roma 149 Dipartimento di Fisica