Related papers: Symplectic integration for the collisional gravita…

We propose a family of integrators, Flow-Composed Implicit Runge-Kutta (FCIRK) methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step…

Using Suzuki-Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special…

We review the recent optimizations of gravitational $N$-body kernels for running them on graphics processing units (GPUs), on single hosts and massive parallel platforms. For each of the two main $N$-body techniques, direct summation and…

Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to…

In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…

An explicit second-order numerical method to integrate the isokinetic equations of motion is derived by fitting circular arcs through every three consecutive points of the discretized trajectory, so that the tangent and the curvature…

Hierarchical code coupling strategies make it possible to combine the results of individual numerical solvers into a self-consistent symplectic solution. We explore the possibility of allowing such a coupling strategy to be non-intrusive.…

Context. Integrating the motion of stars in a smoothed potential is necessary in many stellar and galactic studies. Previous works have often used numerical integrators that alternate between linear drifts and velocity kicks (such as the…

$N$-body simulations study the dynamics of $N$ particles under the influence of mutual long-distant forces such as gravity. In practice, $N$-body codes will violate Newton's third law if they use either an approximate Poisson solver or…

Symplectic integrators offer vastly superior performance over traditional numerical techniques for conservative dynamical systems, but their application to \emph{dissipative} systems is inherently difficult due to dissipative systems' lack…

We report a few sumerical tests comparing some newly defined energy-preserving integrators and symplectic methods, using either constant and variable stepsize.

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…

This paper focuses on the parallel implementation of a direct $N$-body method~(particle-particle algorithm) and the application of multiple GPUs for galactic dynamics simulations. Application of a hybrid OpenMP-CUDA technology is considered…

Energy-correction method is proposed as an addition to mainstream integrators for equations of motion of systems of classical spins. This solves the problem of non-conservation of energy in long computations and makes mainstream integrators…

Several integration schemes exits 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 for…

In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis. It is shown in particular that the new integrators…

This technical report provides an in-depth evaluation of both established and state-of-the-art methods for simulating constrained rigid multi-body systems with hard-contact dynamics, using formulations of Nonlinear Complementarity Problems…

A new type of low-regularity integrator is proposed for Navier-Stokes equations, coupled with a stabilized finite element method in space. Unlike the other low-regularity integrators for nonlinear dispersive equations, which are all fully…

Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators, and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (2015);…

A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves first integrals of the system. The idea is that given an initial point in the manifold…