Related papers: Symplectic methods for non-canonical Hamiltonian s…

This paper is focused on the development of the notions of canonical and canonoid transformations within the framework of Hamiltonian Mechanics on locally conformal symplectic manifolds. Both, time-independent and time-dependent dynamics…

We prove that the recently developed semiexplicit symplectic integrators for non-separable Hamiltonian systems preserve any linear and quadratic invariants possessed by the Hamiltonian systems. This is in addition to being symmetric and…

We present a discrete total variation calculus in Hamiltonian formalism in this paper. Using this discrete variation calculus and generating functions for the flows of Hamiltonian systems, we derive two-step symplectic-energy integrators of…

Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly…

In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…

This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an…

We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time…

A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schr\"odinger-Maxwell equations. The algorithms preserve the symplectic…

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete…

We construct an explicit reversible symplectic integrator for the planar 3-body problem with zero angular momentum. We start with a Hamiltonian of the planar 3-body problem that is globally regularised and fully symmetry reduced. This…

Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity…

We propose a linearly implicit structure-preserving numerical method for semilinear Hamiltonian systems with polynomial nonlinearities, combining Kahan's method and exponential integrator. This approach efficiently balances computational…

In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…

Integrable Hamiltonian systems on almost-symplectic manifolds have recently drawn some attention. Under suitable properties, they have a structure analogous to those of standard symplectic-Hamiltonian completely integrable systems. Here we…

The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the…

We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based…

We present an approach to construct appropriate and efficient emulators for Hamiltonian flow maps. Intended future applications are long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations.…

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we…