Related papers: Variational Formulation of Macro-Particle Models f…
In this paper, we introduce and discuss an exactly energy-conserving Particle-in-Cell method for arbitrary curvilinear coordinates. The flexibility provided by curvilinear coordinates enables the study of plasmas in complex-shaped domains…
In this work we propose a Hybrid method with Deviational Particles (HDP) for a plasma modeled by the inhomogeneous Vlasov-Poisson-Landau system. We split the distribution into a Maxwellian part evolved by a grid based fluid solver and a…
We present a new method for solving the relativistic Vlasov--Maxwell system of equations, applicable to a wide range of extreme high-energy-density astrophysical and laboratory environments. The method directly discretizes the kinetic…
Electromagnetic particle simulation model has been formulated and verified for nonlinear processes of lower hybrid (LH) waves in fusion plasmas. Electron dynamics is described by the drift kinetic equation using either kinetic momentum or…
The present paper develops a variational theory of discrete fields defined on abstract cellular complexes. The discrete formulation is derived solely from a variational principle associated to a discrete Lagrangian density on a discrete…
We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of…
Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vlasov-Maxwell equations that preserves at the discrete level…
We present a deformable Discrete Element Method (DEM) that extends the classical rigid-particle formulation through a reduced-order description of elastic grain-scale deformation. The method hinges on two developments. First, an energetic…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
A variational method for computing conformational properties of molecules with Lennard-Jones potentials for the monomer-monomer interactions is presented. The approach is tailored to deal with angular degrees of freedom, {\it rotors}, and…
The foundations of gyrokinetic theory are reviewed with an emphasis on the applications of Lagrangian and Hamiltonian methods used in the derivation of nonlinear gyrokinetic Vlasov-Maxwell equations. These reduced dynamical equations…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it is needed to consider the effect of external…
A new variational principle for optimizing thermal density matrices is introduced. As a first application, the variational many body density matrix is written as a determinant of one body density matrices, which are approximated by…
This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation for the computation of the self-consistent electric field.…
In recent years, two important techniques for geometric numerical discretization have been developed. In computational electromagnetics, spatial discretization has been improved by the use of mixed finite elements and discrete differential…
A matrix method is formulated in a Lagrangian representation for the solution of the characteristic value problem governing modes of oscillation and instability in a collisionless stellar system. The underlying perturbation equations govern…
We present the standard electromagnetic Particle-in-Cell method, starting from the discrete approximation of derivatives on a uniform grid. The application to second-order, centered, finite-difference discretization of the equations of…