GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
arXiv:1609.03053 · doi:10.1017/S002237781700040X
Abstract
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 properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from Finite Element Exterior Calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the Finite Element basis, as long as the corresponding Finite Element spaces satisfy certain compatibility conditions.
57 Pages
References in corpus (4)
Cited by in corpus (78)
- Structure and structure-preserving algorithms for plasma physics
- Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations
- Structure-Preserving Geometric Particle-in-Cell Methods for Vlasov-Maxwell Systems
- Energy-conserving time propagation for a geometric particle-in-cell Vlasov--Maxwell solver
- Metriplectic Integrators for the Landau Collision Operator
- Finite-dimensional collisionless kinetic theory
- A Low Rank Tensor Representation of Linear Transport and Nonlinear Vlasov Solutions and Their Associated Flow Maps
- A General Metriplectic Framework with Application to Dissipative Extended Magnetohydrodynamics
- Relativistic Extension of a Charge-Conservative Finite Element Solver for Time-Dependent Maxwell-Vlasov Equations
- A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm
- Explicit Structure-Preserving Geometric Particle-in-Cell Algorithm in Curvilinear Orthogonal Coordinate Systems and Its Applications to Whole-Device 6D Kinetic Simulations of Tokamak Physics
- Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories
- Gauge-free electromagnetic gyrokinetic theory
- Detection and Prediction of Equilibrium States in Kinetic Plasma Simulations via Mode Tracking using Reduced-Order Dynamic Mode Decomposition
- The geometric theory of charge conservation in particle-in-cell simulations
- Lagrangian and Dirac constraints for the ideal incompressible fluid and magnetohydrodynamics
- Numerical Electromagnetic Frequency Domain Analysis with Discrete Exterior Calculus
- Magnetohydrodynamic with Adaptively Embedded Particle-in-Cell model: MHD-AEPIC
- Structure-preserving marker-particle discretizations of Coulomb collisions for particle-in-cell codes
- Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics
- Theory and computation of electromagnetic fields and thermomechanical structure interaction for systems undergoing large deformations
- Explicit High-Order Gauge-Independent Symplectic Algorithms for Relativistic Charged Particle Dynamics
- Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence
- Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field
- Rubrics for Charge Conserving Current Mapping in Finite Element Particle in Cell Methods
- Symplectic model reduction methods for the Vlasov equation
- A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles
- Hamiltonian Particle-in-Cell methods for Vlasov-Poisson equations
- Hamiltonian kinetic-Hall Magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes
- Hamiltonian structure of the guiding center plasma model
- Stochastic variational principles for the collisional Vlasov-Maxwell and Vlasov-Poisson equations
- Subcycling of particle orbits in variational, geometric electromagnetic particle-in-cell methods
- Noise and error analysis and optimization in particle-based kinetic plasma simulations
- Geometric Electrostatic Particle-In-Cell Algorithm on Unstructured Meshes
- Advanced fuel fusion, phase space engineering, and structure-preserving geometric algorithms
- An integral transform technique for kinetic systems with collisions
- Reducing Noise for PIC Simulations Using Kernel Density Estimation Algorithm
- Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales
- Multispecies structure-preserving particle discretization of the Landau collision operator
- Hamiltonian reduction of Vlasov-Maxwell to a dark slow manifold
- Metriplectic foundations of gyrokinetic Vlasov-Maxwell-Landau theory
- Energy conserving particle-in-cell methods for relativistic Vlasov--Maxwell equations of laser-plasma interaction
- High order geometric methods with splines: an analysis of discrete Hodge--star operators
- Accelerating Particle-in-Cell Kinetic Plasma Simulations via Reduced-Order Modeling of Space-Charge Dynamics using Dynamic Mode Decomposition
- Quasi-geometric integration of guiding-center orbits in piecewise linear toroidal fields
- Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations
- A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus
- A low-frequency variational model for energetic particle effects in the pressure-coupling scheme
- Splitting methods for Fourier spectral discretizations of the strongly magnetized Vlasov-Poisson and the Vlasov-Maxwell system
- Piecewise Field-Aligned Finite Element Method for Multi-Mode Nonlinear Particle Simulations in tokamak plasmas
- A dual grid geometric electromagnetic particle in cell method
- Variational mean-fluctuation splitting and drift-fluid models
- Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics
- Isogeometric de Rham complex discretization in solid toroidal domains
- Beatification: Flattening the Poisson Bracket for Two-Dimensional Fluid and Plasma Theories
- Numerical Simulations to the Vlasov-Poisson System with a Strong Magnetic Field
- Uniformly accurate methods for three dimensional Vlasov equations under strong magnetic field with varying direction
- Hamiltonian formulation and symplectic split-operator schemes for time-dependent density-functional-theory equations of electron dynamics in molecules
- Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities
- Towards a classification of bifurcations in Vlasov equations
- Variational Schemes and Geometric Simulations for a Hydrodynamic-Electrodynamic Model of Surface Plasmon Polaritons
- Variational formulation of classical and quantum models for intense laser pulse propagation
- Machine learning and serving of discrete field theories -- when artificial intelligence meets the discrete universe
- A structure-preserving finite element framework for the Vlasov-Maxwell system
- Geometric Particle-in-Cell Simulations of the Vlasov--Maxwell System in Curvilinear Coordinates
- Charge-conserving, variational particle-in-cell method for the drift-kinetic Vlasov-Maxwell system
- Symplectic particle-in-cell methods for hybrid plasma models with Boltzmann electrons and space-charge effects
- Higher Order Charge Conserving Electromagnetic Finite Element Particle in Cell Method
- Discrete Gravity with Local Lorentz Invariance
- Adaptive hyper-reduction of non-sparse operators: application to parametric particle-based kinetic plasma models
- Quasi Monte Carlo inverse transform sampling for phase space conserving Lagrangian particle methods and Eulerian-Lagrangian coupling
- A Hybrid Nodal-Staggered Pseudo-Spectral Electromagnetic Particle-In-Cell Method with Finite-Order Centering
- A mimetic discretization of the macroscopic Maxwell equations in Hamiltonian form
- A Hamiltonian model for the macroscopic Maxwell equations using exterior calculus
- Perfect Conductor Boundary Conditions for Geometric Particle-in-Cell Simulations of the Vlasov-Maxwell System in Curvilinear Coordinates
- Gauge-invariant variational formulations of electromagnetic gyrokinetic theory
- Quantum HodgeRank: Topology-Based Rank Aggregation on Quantum Computers
- Extended phase-space symplectic integration for electron dynamics