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The present paper is devoted to the convergence analysis of an asymptotic preserving particle scheme designed to serve as a particle pusher in a Particle-In-Cell (PIC) method for the Vlasov equation with a strong inhomogeneous magnetic…

Numerical Analysis · Mathematics 2025-12-04 Francis Filbet , L Miguel Rodrigues , Kim Han Trinh

First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…

Numerical Analysis · Mathematics 2023-09-08 Jie Ding , Shenggao Zhou

This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in…

Numerical Analysis · Mathematics 2024-11-08 Megala Anandan , Benjamin Boutin , Nicolas Crouseilles

In this paper, Particle-in-Cell algorithms for the Vlasov-Poisson system are presented based on its Poisson bracket structure. The Poisson equation is solved by finite element methods, in which the appropriate finite element spaces are…

Numerical Analysis · Mathematics 2022-08-10 Anjiao Gu , Yang He , Yajuan Sun

For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…

Numerical Analysis · Mathematics 2022-07-04 Stefan Bilbao , Michele Ducceschi , Fabiana Zama

We describe a charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids. Charge conservation is obtained from first principles, i.e., without the need for any post-processing or correction steps. This…

Numerical Analysis · Mathematics 2016-05-04 Haksu Moon , Fernando L. Teixeira , Yuri A. Omelchenko

Hamiltonian particle-based simulations of plasma dynamics are inherently computationally intensive, primarily due to the large number of particles required to obtain accurate solutions. This challenge becomes even more acute in many-query…

Numerical Analysis · Mathematics 2025-06-19 Emmanuel Franck , Laurent Navoret , Vincent Vigon , Raphaël Côte , Guillaume Steimer

We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction, where we focus on the motion of particles in the plane orthogonal to the…

Numerical Analysis · Mathematics 2017-01-25 Francis Filbet , Luis Rodrigues

Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…

Numerical Analysis · Mathematics 2019-06-28 R. Herbin , T. Gallouët , J. -C Latché , N Therme

We consider spherically symmetric, asymptotically flat space-times with a collisionless gas as matter model. Many properties of the resulting Vlasov-Einstein system are not yet accessible by purely analytical means. We present a discretized…

Numerical Analysis · Mathematics 2025-10-20 Gerhard Rein , Thomas Rodewis

We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of…

Numerical Analysis · Mathematics 2020-08-14 Frédéric Marazzato , Alexandre Ern , Christian Mariotti , Laurent Monasse

An electrostatic, implicit particle-in-cell (PIC) model for collisionless, fully magnetized, paraxial plasma expansions in a magnetic nozzle is introduced with exact charge, energy, and magnetic moment conservation properties. The approach…

Plasma Physics · Physics 2024-05-14 Pedro Jimenez , Luis Chacon , Mario Merino

In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic field. When the intensity of the magnetic field is…

Numerical Analysis · Mathematics 2018-05-29 Francis Filbet , Chang Yang

We derive an equation for energy transfer from relativistic charged particles to a cold background plasma appropriate for finite-size particles that are used in particle-in-cell simulation codes. Expressions for one-, two-, and…

We propose a novel reformulation of the Vlasov-Amp{\`e}re equations for plasmas. This reformulation exposes discrete symmetries to achieve simultaneous conservation of mass, momentum, and energy; preservation of Gauss's law involution;…

Plasma Physics · Physics 2024-10-29 William T Taitano , Joshua W Burby , Alex Alekseenko

Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…

Numerical Analysis · Mathematics 2025-12-01 Boris D. Andrews , Patrick E. Farrell

In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stability, and high-order precision to solve the time-dependent…

Numerical Analysis · Mathematics 2025-07-01 Waixiang Cao , Yuzhe Qin , Minqiang Xu

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…

Computational Physics · Physics 2014-04-22 A. B. Stamm , B. A. Shadwick , E. G. Evstatiev

The Vlasov-Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects…

Optimization and Control · Mathematics 2024-07-11 Jan Bartsch , Patrik Knopf , Stefania Scheurer , Jörg Weber

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…

Numerical Analysis · Mathematics 2023-07-10 Jan S. Hesthaven , Cecilia Pagliantini , Nicolò Ripamonti