相关论文: A novel directly energy-preserving method for char…

In this paper, energy-preserving methods are formulated and studied for solving charged-particle dynamics. We first formulate the scheme of energy-preserving methods and analyze its basic properties including algebraic order and symmetry.…

In this paper, we apply the Boole discrete line integral to solve the Lorentz force system which is written as a non-canonical Hamiltonian system. The method is exactly energy-conserving for polynomial Hamiltonians of degree $\nu \leq 4$.…

In this paper, we develop a novel, linearly implicit and local energy-preserving scheme for the sine-Gordon equation. The basic idea is from the invariant energy quadratization approach to construct energy stable schemes for gradient…

We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…

In this paper we study arbitrarily high-order energy-conserving methods for simulating the dynamics of a charged particle. They are derived and studied within the framework of Line Integral Methods (LIMs), previously used for defining…

A novel class of explicit high-order energy-preserving methods are proposed for general Hamiltonian partial differential equations with non-canonical structure matrix. When the energy is not quadratic, it is firstly done that the original…

We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…

We present a novel methodology for constructing arbitrarily high-order structure-preserving methods tailored for damped Hamiltonian systems. This method combines the idea of exponential integrator and energy-preserving collocation methods,…

In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It is based on a suitable…

As is well known, energy is generally deemed as one of the most important physical invariants in many conservative problems and hence it is of remarkable interest to consider numerical methods which are able to preserve it. In this paper,…

The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a retraction, and a coordinate center function. The resulting…

Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that…

In this paper we propose and investigate a general approach to constructing local energy-preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonian PDEs. This approach is based on the temporal…

For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…

Structure-preserving particle methods have recently been proposed for a class of nonlinear continuity equations, including aggregation-diffusion equation in [J. Carrillo, K. Craig, F. Patacchini, Calc. Var., 58 (2019), pp. 53] and the…

A basic leapfrog integrator and its energy-preserving and variational / symplectic variants are proposed and studied for the numerical integration of the equations of motion of relativistic charged particles in an electromagnetic field. The…

We present two novel classes of fully discrete energy-preserving algorithms for the sine-Gordon equation subject to Neumann boundary conditions. The cosine pseudo-spectral method is first used to develop structure-preserving spatial…

In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is…

We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure,…