Related papers: GLISSE: A GPU-optimized planetary system integrato…
Challenging stellar dynamical problems, such as the study of gravothermal oscillations in star clusters, have in the past initiated the very successful building of GRAPE special purpose computers. It is discussed, that present day tasks…
We introduce GRiD: a GPU-accelerated library for computing rigid body dynamics with analytical gradients. GRiD was designed to accelerate the nonlinear trajectory optimization subproblem used in state-of-the-art robotic planning, control,…
We present a novel hierarchical formulation of the fourth-order forward symplectic integrator and its numerical implementation in the GPU-accelerated direct-summation N-body code FROST. The new integrator is especially suitable for…
Elegant is an accelerator physics and particle-beam dynamics code widely used for modeling and design of a variety of high-energy particle accelerators and accelerator-based systems. In this paper we discuss a recently developed version of…
The stability of a galaxy model is most easily assessed through N-body simulation. Particle-mesh codes have been widely used for this purpose, since they enable the largest numbers of particles to be employed. We show that the functional…
The analysis of gravitational wave (GW) datasets is based on the comparison of measured time series with theoretical templates of the detector's response to a variety of source parameters. For LISA, the main scientific observables will be…
Studying the orbital stability of multi-planet systems is essential to understand planet formation, estimate the stable time of an observed planetary system, and advance population synthesis models. Although previous studies have primarily…
Using numerical methods we investigate the dynamical stability of the Gliese 581 exoplanetary system. The system is known to harbour four planets (b-e). The existence of another planet (g) in the liquid water habitable zone of the star is…
By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for…
The large-scale analysis task of deciphering gravitational wave signals in the LISA data stream will be difficult, requiring a large amount of computational resources and extensive development of computational methods. Its high…
This article describes a new, fully adaptive Particle-Multiple-Mesh numerical simulation code developed primarily for simulations of small regions (such as a group of galaxies) in a cosmological context. It integrates the equations of…
We considered the problem of stability for planets of finite mass in binary star systems. We selected a huge set of initial conditions for planetary orbits of the S-type, to perform high precision and very extended in time integrations. For…
We present implementations of a fourth-order symplectic integrator on graphic processing units for three $N$-body models with long-range interactions of general interest: the Hamiltonian Mean Field, Ring and two-dimensional self-gravitating…
We present IAS15, a 15th-order integrator to simulate gravitational dynamics. The integrator is based on a Gau\ss-Radau quadrature and can handle conservative as well as non-conservative forces. We develop a step-size control that can…
Much of standard galaxy dynamics rests on the implicit assumption that the corresponding N-body problem is (near) integrable. This notion although leading to great simplification is by no means a fact. It is therefore important to develop…
Physics simulators are essential in science and engineering, enabling the analysis, control, and design of complex systems. In experimental sciences, they are increasingly used to automate experimental design, often via combinatorial search…
I compare various popular and unpopular techniques for simulating large collisionless stellar systems. I give a quantitative comparison of the raw cpu times required for five separate codes, including tree codes and basis function…
We investigate the possibility that the large orbital eccentricity of the transiting Neptune-mass planet Gliese 436b is maintained in the face of tidal dissipation by a second planet in the system. We find that the currently observed…
In this chapter, we summarize the underlying numerical methods needed for efficient $N$-body integration of planetary systems. We discuss how symplectic integrators have been developed to tackle the complementary problems of long-term…
As a first approximation beyond linearity, the nonlinear Schr\"odinger equation (NLSE) reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally…