# Geometric Particle-in-Cell Simulations of the Vlasov-Maxwell System in Curvilinear Coordinates

@article{Perse2020GeometricPS, title={Geometric Particle-in-Cell Simulations of the Vlasov-Maxwell System in Curvilinear Coordinates}, author={Benedikt Perse and Katharina Kormann and Eric Sonnendr{\"u}cker}, journal={ArXiv}, year={2020}, volume={abs/2111.08342} }

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 the non-canonical Hamiltonian structure of the Vlasov-Maxwell equations has been presented in [Kraus et al. 2017]. Whereas the original formulation has been obtained for Cartesian coordinates, we extend the formulation to curvilinear coordinates in this paper…

## 9 Citations

### Energy conserving particle-in-cell methods for relativistic Vlasov-Maxwell equations of laser-plasma interaction

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### Geometric electrostatic particle-in-cell algorithm on unstructured meshes

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We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this…

### A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

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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…

### 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

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Explicit structure-preserving geometric Particle-in-Cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a crucial further development of the…

### Geometric continuous-stage exponential energy-preserving integrators for charged-particle dynamics in a magnetic field from normal to strong regimes

- MathematicsApplied Numerical Mathematics
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### A broken FEEC framework for electromagnetic problems on mapped multipatch domains

- Mathematics, Computer ScienceArXiv
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We present a framework for the structure-preserving approximation of partial differential equations on mapped multipatch domains, extending the classical theory of finite element exterior calculus…

### Locally-verifiable sufficient conditions for exactness of the hierarchical B-spline discrete de Rham complex in $\mathbb{R}^n$

- Mathematics, Computer Science
- 2022

This work theoretically analyze the discrete de Rham complex built from hierarchical B-spline diﬀerential forms, i.e., the discrete di-erential forms are smooth splines and support adaptive reﬁnements – these properties are key to enabling accurate and e-cient numerical simulations.

### Higher Order Charge Conserving Electromagnetic Finite Element Particle in Cell Method

- Physics
- 2021

Until recently, electromagnetic finite element PIC (EM-FEMPIC) methods that demonstrated charge conservation used explicit field solvers. It is only recently, that a series of papers developed the…

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We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this…

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Explicit structure-preserving geometric Particle-in-Cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a crucial further development of the…

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