共查询到20条相似文献,搜索用时 31 毫秒
1.
Mirek Giersz 《Monthly notices of the Royal Astronomical Society》1998,298(4):1239-1248
A revision of Stodoíkiewicz's Monte Carlo code is used to simulate evolution of star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. The first calculations for isolated, equal-mass N -body systems with three-body energy generation according to Spitzer's formulae show good agreement with direct N -body calculations for N = 2000, 4096 and 10 000 particles. The density, velocity, mass distributions, energy generation, number of binaries, etc., follow the N -body results. Only the number of escapers is slightly too high compared with N -body results, and there is no level-off anisotropy for advanced post-collapse evolution of Monte Carlo models as is seen in N -body simulations for N ≤ 2000. For simulations with N > 10 000 gravothermal oscillations are clearly visible. The calculations of N 2000, 4096, 10 000, 32 000 and 100 000 models take about 2, 6, 20, 130 and 2500 h, respectively. The Monte Carlo code is at least 105 times faster than the N -body one for N = 32 768 with special-purpose hardware. Thus it becomes possible to run several different models to improve statistical quality of the data and run individual models with N as large as 100 000. The Monte Carlo scheme can be regarded as a method which lies in the middle between direct N -body and Fokker–Planck models and combines most advantages of both methods. 相似文献
2.
Several integration schemes exist to solve the equations of motion of the N -body problem. The Lie-integration method is based on the idea to solve ordinary differential equations with Lie-series. In the 1980s, this method was applied to solve the equations of motion of the N -body problem by giving the recurrence formulae for the calculation of the Lie-terms. The aim of this work is to present the recurrence formulae for the linearized equations of motion of N -body systems. We prove a lemma which greatly simplifies the derivation of the recurrence formulae for the linearized equations if the recurrence formulae for the equations of motions are known. The Lie-integrator is compared with other well-known methods. The optimal step-size and order of the Lie-integrator are calculated. It is shown that a fine-tuned Lie-integrator can be 30–40 per cent faster than other integration methods. 相似文献
3.
Seungheon Song C. W. Jung S. Y. Kim Youngbo Choi 《Astrophysics and Space Science》1992,193(2):217-234
TheN-body problem does not have an exact and analytic solution, and computer technique or computer simulation can be a good candidate to solve it. Computing speed in computer simulation is very important. There are many algorithms and computational methods in computer simulation which reduce computer time.In this report a computer simulation model in a cylindrical coordinate, in which the FACR (Fourier Analysis and Cyclic Reduction) method is used, has been proposed and demonstrated the presence of spiral, barred, and ringed galaxy. The method using a cylindrical grid has good symmetrical properties specially for rotating stellar systems. 相似文献
4.
We present a time-transformed leapfrog scheme combined with the extrapolation method to construct an integrator for orbits in N-body systems with large mass ratios. The basic idea can be used to transform any second-order differential equation into a form which may allow more efficient numerical integration. When applied to gravitating few-body systems this formulation permits extremely close two-body encounters to be considered without significant loss of accuracy. The new scheme has been implemented in a direct N-body code for simulations of super-massive binaries in galactic nuclei. In this context relativistic effects may also be included. 相似文献
5.
6.
7.
Davide Farnocchia Giacomo Tommei Andrea Milani Alessandro Rossi 《Celestial Mechanics and Dynamical Astronomy》2010,107(1-2):169-185
We propose two algorithms to provide a full preliminary orbit of an Earth-orbiting object with a number of observations lower than the classical methods, such as those by Laplace and Gauss. The first one is the Virtual debris algorithm, based upon the admissible region, that is the set of the unknown quantities corresponding to possible orbits for a given observation for objects in Earth orbit (as opposed to both interplanetary orbits and ballistic ones). A similar method has already been successfully used in recent years for the asteroidal case. The second algorithm uses the integrals of the geocentric 2-body motion, which must have the same values at the times of the different observations for a common orbit to exist. We also discuss how to account for the perturbations of the 2-body motion, e.g., the J 2 effect. 相似文献
8.
《New Astronomy》2007,12(3):169-181
The main performance bottleneck of gravitational N-body codes is the force calculation between two particles. We have succeeded in speeding up this pair-wise force calculation by factors between 2 and 10, depending on the code and the processor on which the code is run. These speed-ups were obtained by writing highly fine-tuned code for x86_64 microprocessors. Any existing N-body code, running on these chips, can easily incorporate our assembly code programs.In the current paper, we present an outline of our overall approach, which we illustrate with one specific example: the use of a Hermite scheme for a direct N2 type integration on a single 2.0 GHz Athlon 64 processor, for which we obtain an effective performance of 4.05 Gflops, for double-precision accuracy. In subsequent papers, we will discuss other variations, including the combinations of N log N codes, single-precision implementations, and performance on other microprocessors. 相似文献
9.
《New Astronomy》2021
We present an N-body code called Taichi for galactic dynamics and controlled numerical experiments. The code includes two high-order hierarchical multipole expansion methods: the Barnes-Hut (BH) tree and the fast multipole method (FMM). For the time integration, the code can use either a conventional adaptive KDK or a Hamiltonian splitting integrator. The combination of FMM and the Hamiltonian splitting integrator leads to a momentum-conserving N-body scheme with individual time steps. We find Taichi performs well in the typical applications in galactic dynamics. In the isolated and interacting galaxies tests, the momentum conserving scheme produces the same result as a conventional BH tree code. But for similar force accuracies, FMM significantly speeds up the simulations compared to the monopole BH tree. In the cold collapse test, we find the inner structure after relaxation can be sensitive to the force accuracies. Taichi is ready to incorporate special treatment of close encounters thanks to the Hamiltonian splitting integrator, suitable for studying dynamics around central massive bodies. 相似文献
10.
We present a new method for fast numerical integration of close binaries inN-body systems. The basic idea is to slow down the motion of the binary artificially, which makes a faster numerical integration possible but still maintains correct treatment of secular and long-period effects on the motion. We discuss the general principle, with application to close binaries inN-body codes and in the chain regularization. 相似文献
11.
We consider numerical integration of nearly integrable Hamiltonian systems. The emphasis is on perturbed Keplerian motion, such as certain cases of the problem of two fixed centres and the restricted three-body problem. We show that the presently known methods have useful generalizations which are explicit and have a variable physical timestep which adjusts to both the central and perturbing potentials. These methods make it possible to compute accurately fairly close encounters. In some cases we suggest the use of composite (instead of symplectic) alternatives which typically seem to have equally good energy conservation properties.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
12.
Eiichiro Kokubo Keiko Yoshinaga & Junichiro Makino 《Monthly notices of the Royal Astronomical Society》1998,297(4):1067-1072
We describe a P(EC) n Hermite scheme for planetary N -body simulation. The fourth-order implicit Hermite scheme is a time-symmetric integrator that has no secular energy error for the integration of periodic orbits with time-symmetric time-steps. In general N -body problems, however, this advantage is of little practical significance, since it is difficult to achieve time-symmetry with individual variable time-steps. However, we can easily enjoy the benefit of the time-symmetric Hermite integrator in planetary N -body systems, where all bodies spend most of the time on nearly circular orbits. These orbits are integrated with almost constant time-steps even if we adopt the individual time-step scheme. The P(EC) n Hermite scheme and almost constant time-steps reduce the integration error greatly. For example, the energy error of the P(EC)2 Hermite scheme is two orders of magnitude smaller than that of the standard PEC Hermite scheme in the case of an N = 100, m = 1025 g planetesimal system with the rms eccentricity 〈 e 2 〉1/2 ≲0.03. 相似文献
13.
G. Papageorgiou Th. Simos Ch. Tsitouras 《Celestial Mechanics and Dynamical Astronomy》1988,44(1-2):167-177
Explicit Runge-Kutta methods provide a popular way to solve the initial value problem for a system of nonstiff ordinary differential equations. On the other hand, for these methods, there is no a natural way to approximate the solution at any point within a given integration step. Scaled Runge-Kutta methods have been developed recently which determine the solution of the differential system at non-mesh points of a given integration step. We propose some new such algorithms based upon well known explicit Runge-Kutta methods, and we verify their advantages by applying them to the Magnetic-Binary Problem. 相似文献
14.
15.
16.
W. Black 《Celestial Mechanics and Dynamical Astronomy》1973,8(3):357-370
It is shown that in the numerical integration ofN-body problems, as much importance should be given to considerations of the computer programming language to be used as to questions of the accummulation of round-off and truncation error, the stability of the method chosen and the problem being treated. By careful programming processing time may be cut by a factor of 2 or 3 which is an important consideration in extended numerical investigations. The relative usefulness of differing strategies for determining the step size is discussed and in addition the usefulness is shown of treatingN-body problems by a Taylor series method. 相似文献
17.
R. Broucke 《Celestial Mechanics and Dynamical Astronomy》1971,4(1):110-115
A Recurrent Power Series solution is given for the classicalN-body problem. The application to numerical integration is also pointed out. 相似文献
18.
We present a new set of variables for the reduction of the planetary n-body problem, associated to the angular momentum integral, which can be of any use for perturbation theory. The construction of these variables is performed in two steps. A first reduction, called partial is based only on the fixed direction of the angular momentum. The reduction can then be completed using the norm of the angular momentum. In fact, the partial reduction presents many advantages. In particular, we keep some symmetries in the equations of motion (d'Alembert relations). Moreover, in the reduced secular system, we can construct a Birkhoff normal form at any order. Finally, the topology of this problem remains the same as for the non-reduced system, contrarily to Jacobi's reduction where a singularity is present for zero inclinations. For three bodies, these reductions can be done in a very simple way in Poincaré's rectangular variables. In the general n-body case, the reduction can be performed up to a fixed degree in eccentricities and inclinations, using computer algebra expansions. As an example, we provide the truncated expressions for the change of variable in the 4-body case, obtained using the computer algebra system TRIP. 相似文献
19.
András Pál 《Celestial Mechanics and Dynamical Astronomy》2014,119(1):45-54
Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor coefficients of the solution as a set of recurrence relations. In this paper, we present these recurrence formulae for orbital elements and other integrals of motion for the planar $N$ -body problem. We show that if the reference frame is fixed to one of the bodies—for instance to the Sun in the case of the Solar System—the higher order coefficients for all orbital elements and integrals of motion depend only on the mutual terms corresponding to the orbiting bodies. 相似文献
20.
We discuss the main mechanisms affecting the dynamical evolution of Near-Earth Asteroids (NEAs) by analyzing the results of three numerical integrations over 1 Myr of the NEA (4179) Toutatis. In the first integration the only perturbing planet is the Earth. So the evolution is dominated by close encounters and looks like a random walk in semimajor axis and a correlated random walk in eccentricity, keeping almost constant the perihelion distance and the Tisserand invariant. In the second integration Jupiter and Saturn are present instead of the Earth, and the 3/1 (mean motion) and v 6 (secular) resonances substantially change the eccentricity but not the semimajor axis. The third, most realistic, integration including all the three planets together shows a complex interplay of effects, with close encounters switching the orbit between different resonant states and no approximate conservation of the Tisserand invariant. This shows that simplified 3-body or 4-body models cannot be used to predict the typical evolution patterns and time scales of NEAs, and in particular that resonances provide some “fast-track” dynamical routes from low-eccentricity to very eccentric, planet-crossing orbits. 相似文献