Related papers: Symplectic integrators in the shearing sheet
Ising machines are effective solvers for complex combinatorial optimization problems. The idea is mapping the optimal solution(s) to a combinatorial optimization problem to the minimum energy state(s) of a physical system, which naturally…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
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…
Impacts play a fundamental role in shaping the physical and chemical properties of the objects in our Solar System. Given the challenges in replicating such collisions through laboratory experiments, computer simulations are an important…
We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic, momentum preserving, and can be constructed to be of arbitrarily high-order, or can be made to converge…
Mixed-variable symplectic integrators are widely used in orbital dynamics. However, they have been developed for Solar system-type architectures, and can not handle evolving hierarchy, in particular in systems with two or more stellar…
We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the…
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7,…
Two-beam coupling within the field of nonlinear optics, which transfers energy from one light beam to the other under certain conditions, has received considerable attention in inertial confinement fusion (ICF) and plasma optics. To…
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…
We present a reversible and symplectic algorithm called ROLL, for integrating the equations of motion in molecular dynamics simulations of simple fluids on a hypersphere $\mathcal{S}^d$ of arbitrary dimension $d$. It is derived in the…
This paper investigates the equations of motion for a relativistic charged particle in a general magnetic field. By reformulating the dynamics in four-dimensional spacetime and separating the linear and nonlinear parts, we construct an…
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to…
The scattering-adapted flexible inner region ensemble separator (SAFIRES) is a partitioning scheme designed to divide a simulation cell into two regions to be treated with different computational methodologies. SAFIRES prevents particles…
Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…
We give a possible splitting method to a Hamiltonian for the description of charged particles moving around the Reissner-Nordstrom-(anti)-de Sitter black hole with an external magnetic field. This Hamiltonian can be separated into six…
A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D\subseteq X$ and a morphism $\Lambda^{2}E\rightarrow\mathcal{O}_{X}$ satisfying some additional…
We consider Arnoldi like processes to obtain symplectic subspaces for Hamiltonian systems. Large systems are locally approximated by ones living in low dimensional subspaces; we especially consider Krylov subspaces and some extensions. This…
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…
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…