HPC: ASTROPHYSICS AND COSMOLOGY
other computer. ‘At this sort of scale you can double the number of cores and see a drop in performance, because you spend more time waiting for CPUs to communicate with each other than actually doing computation,’ he says, emphasising the need for careful coding.
Peering into the darkness By studying distant clusters of galaxies, astronomers have known of the existence of dark matter for several decades. Without a halo of dark matter around their periphery, galaxies such as our own would not rotate their core so uniformly. The universe’s 100 trillion galaxies, and all of the gasses in between them, account for just 4.6 per cent of its total make-up, with dark matter making up another 22 per cent. The even stranger dark energy makes up the other 74 per cent of the cosmos, driving its accelerating expansion. With so little known about dark matter, and with no way of observing it directly, computer simulations are the only way of determining how it is distributed.
Dr Gavin Pringle is an applications consultant at the Edinburgh Parallel Computing Centre (EPCC), and he works with a virtual community of astrophysicists
called the Virgo project. Simulations run by this group include the Millennium Run, a 100-billion particle simulation carried out in 2005, which gave, at the time, the most comprehensive image to date of the distribution of dark matter in the universe. Pringle explains that the simulation models two kinds of particle, matter and dark matter, with the latter existing as a point mass. In an open system, a single body exerts a force
‘If a two-bodied problem’s chaotic, imagine what a 100-billion body problem would be like!’
on every other body in the system, meaning that doubling the number of particles in the system increases the number of interactions by a factor of four. This is known in computing as the n-body problem, and overcoming it requires the use of approximations. ‘At the heart of any extensive simulation of the universe on an HPC system is the n-body code, modelling cold dark matter. Every element of dark matter needs its x, y and z position, its velocity, and its mass… it’s a
Simple Newtonian problem, but it’s a chaotic system. Some people would say it is impossible to solve,’ says Pringle. ‘Think of a two-bodied problem in which we have two pens joined together: if you hold the end of one and wave it around, then the tip of the bottom pen is completely chaotic. We can’t simulate that. If a two-bodied problem’s chaotic, imagine what a 100-billion body problem would be like!’
This image was generated in 2005 by the Millennium Simulation, by Volker Springel and his group. It shows the distribution of dark matter (in pink) in a halo around a cluster of galaxies. The unit of the scale bar is in megaparsecs, and corresponds to approximately 100 million light-years – one thousand times the diameter of our galaxy. Image: Max Planck Institute for Astrophysics
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A star is mixed Dr Turlough Downes is a lecturer at the School of Mathematical Sciences in Dublin City University, where he is using HPC to study the way in which individual stars form. ‘At the moment, we’re looking at turbulence in a section of a molecular cloud. We know that these clouds really do seem to be turbulent, but we don’t yet understand where the turbulence is coming from, or what the true nature of the turbulence is.’ Stars coalesce from large clouds of gas by the action of gravity, he says, and turbulence in the cloud will compress the gas, aiding star formation. Downes’ multi-fl uid simulation models gasses as fl uids rather than particles: the cloud consists of approximately one unit of charged fl uid for every one million units of uncharged fl uid; charged fl uid will follow magnetic fl ux lines, which result from both the galactic magnetic fi eld and from the charged fl uid itself. Neutral fl uid bumping up against magnetically constrained fl uid will lead to turbulence. ‘We absolutely know that these effects have to be important, because if we don’t include them, then some straightforward back-of-an-envelope calculations show that stars cannot form. We see stars out in the sky, and so clearly stars do form, and so the basic approximations that we use must be wrong. They’re good approximations up to a certain level of accuracy, but beyond that, we need to start using these multi-fl uid effects. We know that they’re important, but we don’t know exactly what they’re going to do.’ In practical terms, high-resolution simulations are required in order to see these effects: ‘You can write down your equations, and you can put them on your computer and solve them, but if you don’t use high enough resolution, you’re not going to capture the multi-fl uid effects.’ The project has been funded by PRACE, and other organisations, and the code has been run on the computers of the Irish Centre for High-End Computing (ICHEC).
SCIENTIFIC COMPUTING WORLD AUGUST/SEPTEMBER 2010
www.scientifi
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