Related papers: Stochastic Discrete Hamiltonian Variational Integr…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamiltonian. We investigate this property from the variational…
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved…
Multisymplectic variational integrators are structure preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and…
Hamiltonian systems are one of the most important class of dynamical systems with a geometric structure called symplecticity and the numerical algorithms which can preserve such geometric structure are of interest. In this article we study…
In this paper, we introduce two types of variational integrators, one originating from the discrete Hamilton's principle while the other from Galerkin variational approach. It turns out that these variational integrators are equivalent to…
It is well known that symplectic integrators lose their near energy preservation properties when variable step sizes are used. The most common approach to combine adaptive step sizes and symplectic integrators involves the Poincar\'e…
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
As is known that various dynamical systems including all Hamiltonian systems preserve volume in phase space. This qualitative geometrical property of the analytical solution should be respected in the sense of Geometric Integration. This…
Variational time integrators are derived in the context of discrete mechanical systems. In this area, the governing equations for the motion of the mechanical system are built following two steps: (a) Postulating a discrete action; (b)…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
In this paper, we consider stochastic Runge-Kutta methods for stochastic Hamiltonian partial differential equations and present some sufficient conditions for multisymplecticity of stochastic Runge-Kutta methods of stochastic Hamiltonian…
We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: preservation of dynamics of certain Casimir and Hamiltonian…
A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their…
Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesis, variational integrators are developed for several…
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…
In this paper, we propose a stochastic conformal multi-symplectic method for a class of damped stochastic Hamiltonian partial differential equations in order to inherit the intrinsic properties, and apply the numerical method to solve a…
A class of Hamiltonian stochastic differential equations with multiplicative L\'{e}vy noise in the sense of Marcus, and the construction and numerical implementation methods of symplectic Euler scheme, are considered. A general symplectic…