Related papers: Variable Timestep Integrators for Long-Term Orbita…
We present a detailed comparison of several integration schemes applied to the dynamic system consisting of a charged particle on the Kerr background endowed with the axisymmetric electromagnetic test field. In particular, we compare the…
We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral…
We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that…
Computational efficiency demands discretised, hierarchically organised, and individually adaptive time-step sizes (known as the block-step scheme) for the time integration of N-body models. However, most existing N-body codes adapt…
Solving quaternion kinematical differential equations is one of the most significant problems in the automation, navigation, aerospace and aeronautics literatures. Most existing approaches for this problem neither preserve the norm of…
We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
The Boris algorithm, a closely related variational integrator and a newly proposed filtered variational integrator are studied when they are used to numerically integrate the equations of motion of a charged particle in a non-uniform strong…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
Multiple time-scale algorithms exploit the natural separation of time-scales in chemical systems to greatly accelerate the efficiency of molecular dynamics simulations. Although the utility of these methods in systems where the interactions…
We investigate the performance of various methods of symplectic integration, which are based on two part splitting of the integration operator, for the numerical integration of multidimensional Hamiltonian systems. We implement these…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
We show that symplectic and linearly-implicit integrators proposed by [Zhang and Skeel, 1997] are variational linearizations of Newmark methods. When used in conjunction with penalty methods (i.e., methods that replace constraints by stiff…
Symplectic tracking of beam particles using point magnets is achieved using a reference orbit made of circular arcs and straight lines that join smoothly with each other. For this choice of the reference orbit, results are given for the…
In this paper, explicit stable integrators based on symplectic and contact geometries are proposed for a non-autonomous ordinarily differential equation (ODE) found in improving convergence rate of Nesterov's accelerated gradient method.…
We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in $\mathbb{R}^3$. Unlike splitting methods, it is defined for all Hamiltonians, and is…
We have proposed new algorithms for the numerical integration of the equations of motion for classical spin systems. In close analogy to symplectic integrators for Hamiltonian equations of motion used in Molecular Dynamics these algorithms…
We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals as standard…
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…