相关论文: Fast and reliable symplectic integration for plane…

We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the…

Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…

Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural…

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 EnckeHH, a new, highly accurate code for orbital dynamics of perturbed Keplerian systems such as planetary systems or galactic centre systems. It solves Encke's equations of motion, which assume perturbed Keplerian orbits. By…

We describe an algorithm for long-term planetary orbit integrations, including the dominant post-Newtonian effects, that employs individual timesteps for each planet. The algorithm is symplectic and exhibits short-term errors that are…

We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational few-body problems. These algorithms have only positive time steps, but require computing the force gradient in…

In this work, we present a symplectic integration scheme to numerically compute space debris motion. Such an integrator is particularly suitable to obtain reliable trajectories of objects lying on high orbits, especially geostationary ones.…

We present the symplectic no-core configuration interaction (SpNCCI) framework, in which the nuclear many-body problem is solved a symmetry-adapted basis that explicitly encodes approximate symmetries associated with nuclear collectivity…

The large dynamic range in some astrophysical N-body problems led to the use of adaptive multi-time-steps; however, the search for optimal strategies is still challenging. We numerically quantify the performance of the hierarchical…

We describe an open source GPU implementation of a hybrid symplectic N-body integrator, GENGA (Gravitational ENcounters with Gpu Acceleration), designed to integrate planet and planetesimal dynamics in the late stage of planet formation and…

This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…

Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…

We report the performance of a newly implemented fourth-order accurate finite-volume HLLC Riemann solver in the adaptive-mesh-refinement numerical relativity code {\tt SACRA-MPI}. First, we validate our implementation in one-dimensional…

We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…

The SecularMultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested…

We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In…

We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We…

Leapfrog integration has been the method of choice in N-body simulations owing to its low computational cost for a symplectic integrator with second order accuracy. We introduce a new leapfrog integrator that allows for variable timesteps…

Many Hamiltonian problems in the Solar System are separable or separate into two analytically solvable parts, and thus give a great chance to the development and application of explicit symplectic integrators based on operator splitting and…