Related papers: Leapfrog methods for relativistic charged-particle…
This paper is concerned with geometric exponential energy-preserving integrators for solving charged-particle dynamics in a magnetic field from normal to strong regimes. We firstly formulate the scheme of the methods for the system in a…
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…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
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…
An extended Hamiltonian approach to conduct isothermal-isobaric molecular dynamics simulations with full cell flexibility is presented. The components of the metric tensor are used as the fictitious degrees of freedom for the cell, thus…
Developing particle-in-cell (PIC) methods using finite element basis sets, and without auxiliary divergence cleaning methods, was a long standing problem until recently. It was shown that if consistent spatial basis functions are used, one…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
We construct a particle integrator for nonrelativistic particles by means of the splitting method based on the exact flow of the equation of motion of particles in the presence of constant electric and magnetic field. This integrator is…
In this paper, we apply the coordinate increment discrete gradient (CIDG) method to solve the Lorentz force system which can be written as a non-canonical Hamiltonian system. Then we can obtain a new energy-preserving CIDG-I method for the…
Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
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…
We describe a new hybrid framework to model non-thermal spectral signatures from highly energetic particles embedded in a large-scale classical or relativistic MHD flow. Our method makes use of \textit{Lagrangian} particles moving through…
The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants. We give strong numerical evidence that alternative, easy to implement algorithms yield fewer rejections with a given computational effort.…
Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the…
The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper,…
Closed nonrelativistic (nonretarded) theory of conservative and dissipative electromagnetic forces and heat exchange between moving particles (nanoprobes) and a surface (flat and cylindrical) is reviewed. The formalism is based on methods…
Lorentz invariant structure-preserving algorithms possess reference-independent secular stability, which is vital for simulating relativistic multi-scale dynamical processes. The splitting method has been widely used to construct…
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…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…