Related papers: Explicit high-order non-canonical symplectic parti…
Variational symplectic algorithms have recently been developed for carrying out long-time simulation of charged particles in magnetic fields. As a direct consequence of their derivation from a discrete variational principle, these…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of…
The Vlasov-Poisson equations describe the evolution of a collisionless plasma, represented through a probability density function (PDF) that self-interacts via an electrostatic force. One of the main difficulties in numerically solving this…
We present an efficient and accurate energy-conserving implicit particle-in-cell~(PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple…
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,…
We present the Photon-Plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation…
We present a novel framework for Finite Element Particle-in-Cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining…
We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…
We introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC…
This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…
We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
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…
We propose an arbitrarily higher (even) order implicit leapfrog scheme for time discretization of a three-field formulation of Maxwell's equations. We use this in conjunction with an arbitrarily higher-order and compatible discretization…
We present a dequantization algorithm for the Vlasov--Poisson (VP) system, termed the dequantized particle algorithm, by systematically dequantizing the underlying many-body quantum theory. Starting from the second-quantized Hamiltonian…
Existing approaches to solving the Vlasov equation treat the system as a partial differential equation on a phase space grid, and track in either an Eulerian, Lagrangian, or semi-Lagrangian picture. We present an alternative approach, which…
The traditional explicit electrostatic momentum-conserving Particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical accuracy. The explicit electrostatic energy-conserving Particle-in-Cell…
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…