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Register a new userN-Body Simulations on GPUs
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Added by
Eric Darve
Publication date
2007
fields
Informatics Engineering
and research's language is
English
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Commercial graphics processors (GPUs) have high compute capacity at very low cost, which makes them attractive for general purpose scientific computing. In this paper we show how graphics processors can be used for N-body simulations to obtain improvements in performance over current generation CPUs. We have developed a highly optimized algorithm for performing the O(N^2) force calculations that constitute the major part of stellar and molecular dynamics simulations. In some of the calculations, we achieve sustained performance of nearly 100 GFlops on an ATI X1900XTX. The performance on GPUs is comparable to specialized processors such as GRAPE-6A and MDGRAPE-3, but at a fraction of the cost. Furthermore, the wide availability of GPUs has significant implications for cluster computing and distributed computing efforts like Folding@Home.
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This work arises on the environment of the ExaNeSt project aiming at design and development of an exascale ready supercomputer with low energy consumption profile but able to support the most demanding scientific and technical applications. The ExaNeSt compute unit consists of densely-packed low-power 64-bit ARM processors, embedded within Xilinx FPGA SoCs. SoC boards are heterogeneous architecture where computing power is supplied both by CPUs and GPUs, and are emerging as a possible low-power and low-cost alternative to clusters based on traditional CPUs. A state-of-the-art direct $N$-body code suitable for astrophysical simulations has been re-engineered in order to exploit SoC heterogeneous platforms based on ARM CPUs and embedded GPUs. Performance tests show that embedded GPUs can be effectively used to accelerate real-life scientific calculations, and that are promising also because of their energy efficiency, which is a crucial design in future exascale platforms.
The general consensus in the N-body community is that statistical results of an ensemble of collisional N-body simulations are accurate, even though individual simulations are not. A way to test this hypothesis is to make a direct comparison of an ensemble of solutions obtained by conventional methods with an ensemble of true solutions. In order to make this possible, we wrote an N-body code called Brutus, that uses arbitrary-precision arithmetic. In combination with the Bulirsch--Stoer method, Brutus is able to obtain converged solutions, which are true up to a specified number of digits. We perform simulations of democratic 3-body systems, where after a sequence of resonances and ejections, a final configuration is reached consisting of a permanent binary and an escaping star. We do this with conventional double-precision methods, and with Brutus; both have the same set of initial conditions and initial realisations. The ensemble of solutions from the conventional simulations is compared directly to that of the converged simulations, both as an ensemble and on an individual basis to determine the distribution of the errors. We find that on average at least half of the conventional simulations diverge from the converged solution, such that the two solutions are microscopically incomparable. For the solutions which have not diverged significantly, we observe that if the integrator has a bias in energy and angular momentum, this propagates to a bias in the statistical properties of the binaries. In the case when the conventional solution has diverged onto an entirely different trajectory in phase-space, we find that the errors are centred around zero and symmetric; the error due to divergence is unbiased, as long as the time-step parameter, eta <= 2^(-5) and when simulations which violate energy conservation by more than 10% are excluded.
Extensions to the C++ implementation of the QCD Data Parallel Interface are provided enabling acceleration of expression evaluation on NVIDIA GPUs. Single expressions are off-loaded to the device memory and execution domain leveraging the Portable Expression Template Engine and using Just-in-Time compilation techniques. Memory management is automated by a software implementation of a cache controlling the GPUs memory. Interoperability with existing Krylov space solvers is demonstrated and special attention is paid on Chroma readiness. Non-kernel routines in lattice QCD calculations typically not subject of hand-tuned optimisations are accelerated which can reduce the effects otherwise suffered from Amdahls Law.
Gravitational N-body simulations, that is numerical solutions of the equations of motions for N particles interacting gravitationally, are widely used tools in astrophysics, with applications from few body or solar system like systems all the way up to galactic and cosmological scales. In this article we present a summary review of the field highlighting the main methods for N-body simulations and the astrophysical context in which they are usually applied.
Triangle counting is a building block for a wide range of graph applications. Traditional wisdom suggests that i) hashing is not suitable for triangle counting, ii) edge-centric triangle counting beats vertex-centric design, and iii) communication-free and workload balanced graph partitioning is a grand challenge for triangle counting. On the contrary, we advocate that i) hashing can help the key operations for scalable triangle counting on Graphics Processing Units (GPUs), i.e., list intersection and graph partitioning, ii)vertex-centric design reduces both hash table construction cost and memory consumption, which is limited on GPUs. In addition, iii) we exploit graph and workload collaborative, and hashing-based 2D partitioning to scale vertex-centric triangle counting over 1,000 GPUswith sustained scalability. In this work, we present TRUST which performs triangle counting with the hash operation and vertex-centric mechanism at the core. To the best of our knowledge, TRUSTis the first work that achieves over one trillion Traversed Edges Per Second (TEPS) rate for triangle counting.
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