A structure-preserving spline finite element solver for the cold-plasma model

¹ Max Planck Institute for Plasma Physics, Garching, Germany.
² Department of Mathematics, Technical University of Munich

^* Corresponding author: elena.moral.sanchez@ipp.mpg.de
^** Corresponding author: martin.campos-pinto@ipp.mpg.de
^*** Corresponding author: yaman.guclu@ipp.mpg.de
^**** Corresponding author: omar.maj@ipp.mpg.de

Published online: 7 January 2026

Abstract

We present a spline finite element solver, which preserves the Hamiltonian structure of the coldplasma model as well as several physical invariants, such as the energy, the total charge and the zero divergence of the magnetic field. The scheme is naturally adapted to Cartesian and curvilinear geometries. A key feature of the scheme is that in the presence of a time-harmonic source, it is consistent with a high-order approximation of the associated time-harmonic solution: this makes the solver intrinsically stable and long simulation runs cannot develop unphysical effects. Our implementation relies on PSYDAC, an isogeometric B-splines finite-element library that can be used to build efficient solvers based on modern numerical methods. In this paper we include an overview of the library and present an example of implementation.