A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus
arXiv:2110.10346 · doi:10.1017/S0022377822000290
Abstract
A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to the class of gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via the momentum map. We numerically demonstrate this time invariance of the momentum map and its usefulness in establishing precise initial conditions with a desired initial electric field and fixed background charge. The restriction of this canonical, finite element Poisson structure to the 1X2P phase space is also considered and simulated numerically.
References in corpus (24)
- Finite element exterior calculus: from Hodge theory to numerical stability
- GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
- Structure and structure-preserving algorithms for plasma physics
- Variational formulation of particle algorithms for kinetic plasma simulations
- Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
- A Hamiltonian splitting for the Vlasov-Maxwell system
- Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
- Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov-Maxwell system
- Exact Charge-Conserving Scatter-Gather Algorithm for Particle-in-Cell Simulations on Unstructured Grids: A Geometric Perspective
- Finite element differential forms on cubical meshes
- Structure-Preserving Geometric Particle-in-Cell Methods for Vlasov-Maxwell Systems
- Hamiltonian integration methods for Vlasov-Maxwell equations
- Energy-conserving time propagation for a geometric particle-in-cell Vlasov--Maxwell solver
- Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
- Metriplectic Integrators for the Landau Collision Operator
- Finite element differential forms on curvilinear cubic meshes and their approximation properties
- Finite-dimensional collisionless kinetic theory
- 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
- The geometric theory of charge conservation in particle-in-cell simulations
- Comment on "Hamiltonian splitting for the Vlasov-Maxwell equations"
- Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence
- Time Integrator Agnostic Charge Conserving Finite Element PIC
- Subcycling of particle orbits in variational, geometric electromagnetic particle-in-cell methods
- Geometric Electrostatic Particle-In-Cell Algorithm on Unstructured Meshes