Related papers: Long term analysis of splitting methods for charge…
We describe a novel splitting approach to numerical relativistic magnetohydrodynamics (RMHD) designed to expand its applicability to the domain of ultra-high magnetisation (high-$\sigma$). In this approach, the electromagnetic field is…
Describing long-ranged electrostatics using short-ranged pair potentials is appealing since the computational complexity scales linearly with the number of particles. The foundation of this approach is to mimic the long-ranged medium…
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…
This study applies response theory to investigate electron charge dynamics, with a particular focus on charge separation. We analytically assess the strengths and limitations of linear and quadratic response theories in describing charge…
In this paper we present a model based on dynamics of the electrons in the plasma using a simplified Boltzmann equation coupled with a Poisson equation. The motivation arose to simulate active plasma resonance spectroscopy which is used for…
Adiabatic invariants are fundamental to plasma physics but are often treated as purely theoretical concepts in undergraduate courses due to the difficulty of experimentally demonstrating them. This paper presents a pedagogical experiment to…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical…
The double distribution function approach is an efficient route towards extension of kinetic solvers to compressible flows. With a number of realizations available, an overview and comparative study in the context of high speed compressible…
In this paper, we study the charged-particle dynamics under strong magnetic field in a toroidal axi-symmetric geometry. Using modulated Fourier expansions of the exact and numerical solutions, the long-term drift motion of the exact…
In this paper an asymptotic expansion of the global error on the stepsize for partitioned linear multistep methods is proved. This provides a tool to analyse the behaviour of these integrators with respect to error growth with time and…
In this paper, we develop two energy-preserving splitting methods for solving three-dimensional stochastic Maxwell equations driven by multiplicative noise. We use operator splitting methods to decouple stochastic Maxwell equations into…