Gravity Pipe (abbreviated GRAPE) is a project which uses hardware acceleration to perform gravitational computations. Integrated with Beowulf-style commodity computers, the GRAPE system calculates the force of gravity that a given mass, such as a star, exerts on others. [1] The project resides at University of Tokyo.
The GRAPE hardware acceleration component "pipes" the force computation to the general-purpose computer serving as a node in a parallelized cluster as the innermost loop of the gravitational model.
The GRAPE project designed an ASIC component with mathematical logic and operations to generate the required computations. This means the latter generations of GRAPE supercomputers, despite not providing a Turing complete computational processing power, are powerful for heavily mathematical super-computing usages. The MD-GRAPE 3 supercomputer was also used in protein folding simulations.
Its shortened name, GRAPE, was chosen as an intentional reference to the Apple Inc. line of computers. [1]
The primary calculation in GRAPE hardware is a summation of the forces between a particular star and every other star in the simulation.
Several versions (GRAPE-1, GRAPE-3 and GRAPE-5) use the logarithmic number system (LNS) in the pipeline to calculate the approximate force between two stars and take the antilogarithms of the x, y and z components before adding them to their corresponding total. [2] The GRAPE-2, GRAPE-4 and GRAPE-6 use floating-point arithmetic for more accurate calculation of such forces. The advantage of the logarithmic-arithmetic versions is that they allow more and faster parallel pipes for a given hardware cost because all but the sum portion of the GRAPE algorithm (1.5 power of the sum of the squares of the input data divided by the input data) is easy to perform with LNS.
GRAPE-DR consists of a large number of simple processors, all operating in the SIMD fashion. [3]
GRAPE computes approximate solutions to the historically intractable n-body problem, which is of interest in astrophysics and celestial mechanics. n refers to the number of celestial bodies in a given problem. While the 2-body problem was solved by Kepler's laws in the 17th century, any calculation where n > 2 has historically been a nigh-impossible challenge. An analytical solution exists for n = 3, although the resulting series converges too slowly to be of practical use. For n > 2, solutions are generally calculated numerically by determining the interaction between all particles. Thus, the calculation scales as n2.
GRAPE assists in calculations of interactions between particles where the interaction scales as r−2. This dependence is hardwired, drastically improving calculation times. These problems include the evolution of galaxies (gravitation force scales as r−2). Similar problems exist in molecular chemistry and biology, where the force considered would be electrical rather than gravitational.
In 1999, Marseilles Observatory published a study on simulating the formation of proto-planets and plantessimals with a large planetary body. [4] This simulation used the GRAPE-4 system. [4]
The LNS-based GRAPE-5 architecture won the Price Performance category of the Gordon Bell Prize in 1999, at about $7 per MegaFLOPS. This category measures the price efficiency of a particular machine in terms of the price in dollars per megaFLOPS. The particular implementation "Grape-6" also won prizes in 2000 and 2001 (see external links). Grape-DR was ranked first in the June 2010 Little Green500 List, [5] a ranking of supercomputer's performance per unit power consumption published by the Green500.org. [6]
A supercomputer is a type of computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS). Since 2022, supercomputers have existed which can perform over 1018 FLOPS, so called exascale supercomputers. For comparison, a desktop computer has performance in the range of hundreds of gigaFLOPS (1011) to tens of teraFLOPS (1013). Since November 2017, all of the world's fastest 500 supercomputers run on Linux-based operating systems. Additional research is being conducted in the United States, the European Union, Taiwan, Japan, and China to build faster, more powerful and technologically superior exascale supercomputers.
Computational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics — an area of study which supplements both theory and experiment.
Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Separated objects attract and are attracted as if all their mass were concentrated at their centers. The publication of the law has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.
An approximation is anything that is intentionally similar but not exactly equal to something else.
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Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered.
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science, and more specifically the Computer Sciences, which uses advanced computing capabilities to understand and solve complex physical problems. While this discussion typically extenuates into Visual Computation, this research field of study will typically include the following research categorizations.
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Norman Howard Christ is a physicist and professor at Columbia University, where he holds the Ephraim Gildor Professorship of Computational Theoretical Physics. He is notable for his research in Lattice QCD.
In physics and astronomy, an N-body simulation is a simulation of a dynamical system of particles, usually under the influence of physical forces, such as gravity. N-body simulations are widely used tools in astrophysics, from investigating the dynamics of few-body systems like the Earth-Moon-Sun system to understanding the evolution of the large-scale structure of the universe. In physical cosmology, N-body simulations are used to study processes of non-linear structure formation such as galaxy filaments and galaxy halos from the influence of dark matter. Direct N-body simulations are used to study the dynamical evolution of star clusters.
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing.
In computing, performance per watt is a measure of the energy efficiency of a particular computer architecture or computer hardware. Literally, it measures the rate of computation that can be delivered by a computer for every watt of power consumed. This rate is typically measured by performance on the LINPACK benchmark when trying to compare between computing systems: an example using this is the Green500 list of supercomputers. Performance per watt has been suggested to be a more sustainable measure of computing than Moore's Law.
The Center for Computational Relativity and Gravitation (CCRG) is a research center of the College of Science (COS) and a Research Center of Excellence at Rochester Institute of Technology (RIT) dedicated to research at the frontiers of numerical relativity and relativistic astrophysics, gravitational-wave physics, its connection to experiments and observations, and high-performance computation and scientific visualization.
gravitySimulator is a novel supercomputer that incorporates special-purpose GRAPE hardware to solve the gravitational n-body problem. It is housed in the Center for Computational Relativity and Gravitation (CCRG) at the Rochester Institute of Technology. It became operational in 2005.
In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. In the 20th century, understanding the dynamics of globular cluster star systems became an important n-body problem. The n-body problem in general relativity is considerably more difficult to solve due to additional factors like time and space distortions.
The Sidney Fernbach Award established in 1992 by the IEEE Computer Society, in memory of Sidney Fernbach, one of the pioneers in the development and application of high performance computers for the solution of large computational problems as the Division Chief for the Computation Division at Lawrence Livermore Laboratory from the late 1950s through the 1970s. A certificate and $2,000 are awarded for outstanding contributions in the application of high performance computers using innovative approaches. The nomination deadline is 1 July each year.
Japan operates a number of centers for supercomputing which hold world records in speed, with the K computer being the world's fastest from June 2011 to June 2012, and Fugaku holding the lead from June 2020 until June 2022.
Computational astrophysics refers to the methods and computing tools developed and used in astrophysics research. Like computational chemistry or computational physics, it is both a specific branch of theoretical astrophysics and an interdisciplinary field relying on computer science, mathematics, and wider physics. Computational astrophysics is most often studied through an applied mathematics or astrophysics programme at PhD level.
Titan or OLCF-3 was a supercomputer built by Cray at Oak Ridge National Laboratory for use in a variety of science projects. Titan was an upgrade of Jaguar, a previous supercomputer at Oak Ridge, that uses graphics processing units (GPUs) in addition to conventional central processing units (CPUs). Titan was the first such hybrid to perform over 10 petaFLOPS. The upgrade began in October 2011, commenced stability testing in October 2012 and it became available to researchers in early 2013. The initial cost of the upgrade was US$60 million, funded primarily by the United States Department of Energy.