Time-splitting methods for the cold-plasma model using Finite Element Exterior Calculus

TL;DR

This paper introduces a high-order, structure-preserving finite element method for the cold plasma model using exterior calculus, with stable time-splitting integrators suitable for complex geometries and long-term simulations.

Contribution

It develops a novel finite element discretization that preserves Hamiltonian structure and implements stable time-splitting schemes for efficient plasma wave simulations.

Findings

The proposed methods are more accurate and cost-effective than standard schemes.

They demonstrate long-term stability in complex geometries.

The Python library Psydac enables efficient, parallel, three-dimensional simulations.

Abstract

In this work we propose a high-order structure-preserving discretization of the cold plasma model which describes the propagation of electromagnetic waves in magnetized plasmas. By utilizing B-Splines Finite Elements Exterior Calculus, we derive a space discretization that preserves the underlying Hamiltonian structure of the model, and we study two stable time-splitting geometrical integrators. We approximate an incoming wave boundary condition in such a way that the resulting schemes are compatible with a time-harmonic / transient decomposition of the solution, which allows us to establish their long-time stability. This approach readily applies to curvilinear and complex domains. We perform a numerical study of these schemes which compares their cost and accuracy against a standard Crank-Nicolson time integrator, and we run realistic simulations where the long-term behaviour is assessed using frequency-domain solutions. Our solvers are implemented in the Python library Psydac which makes them memory-efficient, parallel and essentially three-dimensional.