Related papers: Helicity-preserving finite element discretization …
Two setups with interlocked magnetic flux tubes are used to study the evolution of magnetic energy and helicity on magnetohydrodynamical (MHD) systems like plasmas. In one setup the initial helicity is zero while in the other it is finite.…
Magnetic fields of laboratory, planetary, stellar, and galactic plasmas commonly exhibit significant order on large temporal or spatial scales compared to the otherwise random motions within the hosting system. Such ordered fields can be…
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
We present a structure-preserving discretization of the hybrid magnetohydrodynamics (MHD)-driftkinetic system for simulations of low-frequency wave-particle interactions. The model equations are derived from a variational principle,…
We develop a structure-preserving numerical discretization for the electrostatic Euler-Poisson equations with a constant magnetic field. The scheme preserves positivity of the density, positivity of the internal energy and a minimum…
Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…
The recent years have witnessed an emergence of the field of all-spin-based devices without any flow of charge. An ultimate goal of this scientific direction is the realization of full spectrum of spin-based networks like in modern…
Hamiltonian and action principle (HAP) formulations of plasma physics are reviewed for the purpose of explaining structure preserving numerical algorithms. Geometric structures associated with and emergent from HAP formulations are…
In this paper a relaxation theory, proposed several years ago for plasmas where a single dominant mode is present, is revisited. The solutions of the related eigenvalue problem are numerically calculated and discussed. Although these…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
The dual symmetry between the electric and magnetic fields underlies Maxwell's electrodynamics. Due to this symmetry one can describe topological properties of an electromagnetic field in free space and obtain the conservation law of…
Models for astrophysical plasmas often have magnetic field lines that leave the boundary rather than closing within the computational domain. Thus, the relative magnetic helicity is frequently used in place of the usual magnetic helicity,…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
For magnetic knots and links in plasmas we introduce an internal twist and study their dynamical behavior in numerical simulations. We use a set of helical and non-helical configurations and add an internal twist that cancels the helicity…
The parabolic-elliptic Keller-Segel equation with sensitivity saturation, because of its pattern formation ability, is a challenge for numerical simulations. We provide two finite-volume schemes whose goals are to preserve, at the discrete…
We outline how discrete analogues of the conservation of potential vorticity may be achieved in Finite Element numerical schemes for a variational system which has the particle relabelling symmetry, typically shallow water equations. We…
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite…