Systolic and Hyper-Systolic Algorithms for the Gravitational N-Body Problem, with an Application to Brownian Motion

A systolic algorithm rhythmically computes and passes data through a network of processors. We investigate the performance of systolic algorithms for implementing the gravitational N-body problem on distributed-memory computers. Systolic algorithms minimize memory requirements by distributing the particles between processors. We show that the performance of systolic routines can be greatly enhanced by the use of non-blocking communication, which allows particle coordinates to be communicated at the same time that force calculations are being carried out. Hyper-systolic algorithms reduce the communication complexity at the expense of increased memory demands. As an example of an application requiring large N, we use the systolic algorithm to carry out direct-summation simulations using 10^6 particles of the Brownian motion of the supermassive black hole at the center of the Milky Way galaxy. We predict a 3D random velocity of 0.4 km/s for the black hole.Comment: 33 pages, 10 postscript figure

Distributed N-body Simulation on the Grid Using Dedicated Hardware

We present performance measurements of direct gravitational N -body simulation on the grid, with and without specialized (GRAPE-6) hardware. Our inter-continental virtual organization consists of three sites, one in Tokyo, one in Philadelphia and one in Amsterdam. We run simulations with up to 196608 particles for a variety of topologies. In many cases, high performance simulations over the entire planet are dominated by network bandwidth rather than latency. With this global grid of GRAPEs our calculation time remains dominated by communication over the entire range of N, which was limited due to the use of three sites. Increasing the number of particles will result in a more efficient execution. Based on these timings we construct and calibrate a model to predict the performance of our simulation on any grid infrastructure with or without GRAPE. We apply this model to predict the simulation performance on the Netherlands DAS-3 wide area computer. Equipping the DAS-3 with GRAPE-6Af hardware would achieve break-even between calculation and communication at a few million particles, resulting in a compute time of just over ten hours for 1 N -body time unit. Key words: high-performance computing, grid, N-body simulation, performance modellingComment: (in press) New Astronomy, 24 pages, 5 figure

A pilgrimage to gravity on GPUs

In this short review we present the developments over the last 5 decades that have led to the use of Graphics Processing Units (GPUs) for astrophysical simulations. Since the introduction of NVIDIA's Compute Unified Device Architecture (CUDA) in 2007 the GPU has become a valuable tool for N-body simulations and is so popular these days that almost all papers about high precision N-body simulations use methods that are accelerated by GPUs. With the GPU hardware becoming more advanced and being used for more advanced algorithms like gravitational tree-codes we see a bright future for GPU like hardware in computational astrophysics.Comment: To appear in: European Physical Journal "Special Topics" : "Computer Simulations on Graphics Processing Units" . 18 pages, 8 figure

Performance analysis of direct N-body algorithms for astrophysical simulations on distributed systems

We discuss the performance of direct summation codes used in the simulation of astrophysical stellar systems on highly distributed architectures. These codes compute the gravitational interaction among stars in an exact way and have an O(N^2) scaling with the number of particles. They can be applied to a variety of astrophysical problems, like the evolution of star clusters, the dynamics of black holes, the formation of planetary systems, and cosmological simulations. The simulation of realistic star clusters with sufficiently high accuracy cannot be performed on a single workstation but may be possible on parallel computers or grids. We have implemented two parallel schemes for a direct N-body code and we study their performance on general purpose parallel computers and large computational grids. We present the results of timing analyzes conducted on the different architectures and compare them with the predictions from theoretical models. We conclude that the simulation of star clusters with up to a million particles will be possible on large distributed computers in the next decade. Simulating entire galaxies however will in addition require new hybrid methods to speedup the calculation.Comment: 22 pages, 8 figures, accepted for publication in Parallel Computin

N-body gravitational and contact dynamics for asteroid aggregation

The development of dedicated numerical codes has recently pushed forward the study of N-body gravitational dynamics, leading to a better and wider understanding of processes involving the formation of natural bodies in the Solar System. A major branch includes the study of asteroid formation: evidence from recent studies and observations support the idea that small and medium size asteroids between 100 m and 100 km may be gravitational aggregates with no cohesive force other than gravity. This evidence implies that asteroid formation depends on gravitational interactions between different boulders and that asteroid aggregation processes can be naturally modeled with N-body numerical codes implementing gravitational interactions. This work presents a new implementation of an N-body numerical solver. The code is based on Chrono::Engine (2006). It handles the contact and collision of large numbers of complex-shaped objects, while simultaneously evaluating the effect of N to N gravitational interactions. A special case of study is considered, investigating the relative dynamics between the N bodies and highlighting favorable conditions for the formation of a stable gravitationally bound aggregate from a cloud of N boulders. The code is successfully validated for the case of study by comparing relevant results obtained for typical known dynamical scenarios. The outcome of the numerical simulations shows good agreement with theory and observation, and suggests the ability of the developed code to predict natural aggregation phenomena

Performance Analysis of Direct N-Body Algorithms on Special-Purpose Supercomputers

Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N^2). Performance can be greatly enhanced via the use of special-purpose accelerator boards like the GRAPE-6A. However the memory of the GRAPE boards is limited. Here, we present a performance analysis of direct N-body codes on two parallel supercomputers that incorporate special-purpose boards, allowing as many as four million particles to be integrated. Both computers employ high-speed, Infiniband interconnects to minimize communication overhead, which can otherwise become significant due to the small number of "active" particles at each time step. We find that the computation time scales well with processor number; for 2*10^6 particles, efficiencies greater than 50% and speeds in excess of 2 TFlops are reached.Comment: 34 pages, 15 figures, submitted to New Astronom

Computing and analyzing gravitational radiation in black hole simulations using a new multi-block approach to numerical relativity

Numerical simulations of Kerr black holes are presented and the excitation of quasinormal modes is studied in detail. Issues concerning the extraction of gravitational waves from numerical space-times and analyzing them in a systematic way are discussed. A new multi-block infrastructure for solving first order symmetric hyperbolic time dependent partial differential equations is developed and implemented in a way that stability is guaranteed for arbitrary high order accurate numerical schemes. Multi-block methods make use of several coordinate patches to cover a computational domain. This provides efficient, flexible and very accurate numerical schemes. Using this code, three dimensional simulations of perturbed Kerr black holes are carried out. While the quasinormal frequencies for such sources are well known, until now little attention has been payed to the relative excitation strength of different modes. If an actual perturbed Kerr black hole emits two distinct quasinormal modes that are strong enough to be detected by gravitational wave observatories, these two modes can be used to test the Kerr nature of the source. This would provide a strong test of the so called no hair theorem of general relativity. A systematic method for analyzing ringdown waveforms is proposed. The so called time shift problem, an ambiguity in the definition of excitation amplitudes, is identified and it is shown that this problem can be avoided by looking at appropriately chosen relative mode amplitudes. Rotational mode coupling, the relative excitation strength of co- and counter rotating modes and overtones for slowly and rapidly spinning Kerr black holes are studied. A method for extracting waves from numerical space-times which generalizes one of the standard methods based on the Regge-Wheeler-Zerilli perturbation formalism is presented. Applying this to evolutions of single perturbed Schwarzschild black holes, the accuracy of the new method is compared to the standard approach and it is found that the errors resulting from the former are one to several orders of magnitude below the ones from the latter. It is demonstrated that even at large extraction radii (r=80M), the standard extraction approach produces errors that are dominantly of systematic nature and not due to numerical inaccuracies

The gravitational billion body problem : Het miljard deeltjes probleem

The increased availability of accelerator technology in modern supercomputers forces users to redesign their algorithms. These accelerators are specifically designed to offer huge amounts of parallel compute power. In this thesis I show how to harness the power of these parallel processors for astrophysical simulations. I start with an introduction that presents the developments in astrophysical algorithms and used hardware since the 1960__s till today. In the following scientific chapters I discuss the use of GPU accelerator technology for direct N-body methods and for the more advanced hierarchical algorithms. These advanced algorithms are more complex to implement on large parallel architectures, but by redesigning the algorithms it is possible to take advantage of the GPU. The developed algorithms are applied to simulate galaxy mergers to explain discrepancies in observational results. In the simulations we test different merger configurations and try to match the results with observational data. The final chapter shows how to scale the developed software code to thousands of GPUs as available in the Titan supercomputer. The in this thesis developed and presented algorithms allow astronomers to take advantage of the new GPU technology and thereby run simulations that contain thousand times more particles than was possible beforeNWOUBL - phd migration 201

Multibody dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: Formulations and Numerical Methods, Efficient Methods and Real-Time Applications, Flexible Multibody Dynamics, Contact Dynamics and Constraints, Multiphysics and Coupled Problems, Control and Optimization, Software Development and Computer Technology, Aerospace and Maritime Applications, Biomechanics, Railroad Vehicle Dynamics, Road Vehicle Dynamics, Robotics, Benchmark Problems. The conference is organized by the Department of Mechanical Engineering of the Universitat Politècnica de Catalunya (UPC) in Barcelona. The organizers would like to thank the authors for submitting their contributions, the keynote lecturers for accepting the invitation and for the quality of their talks, the awards and scientific committees for their support to the organization of the conference, and finally the topic organizers for reviewing all extended abstracts and selecting the awards nominees.Postprint (published version