Variational Framework for Structure-Preserving Electromagnetic Particle-in-Cell Methods

Abstract In this article we apply a discrete action principle for the Vlasov–Maxwell equations in structure-preserving particle-field discretization framework. framework finite-dimensional electromagnetic potentials and fields are represented de Rham sequence involving general finite element spaces, coupling is by set of projection operators that commute with differential operators. With minimal number assumptions which allow variety elements shape functions particles, show resulting variational scheme has Poisson structure thus leads to semi-discrete Hamiltonian system. By introducing interior products derive second type space momentum preserving, based on same functions. We illustrate our method applying it spline elements, new spectral where relies Fourier transforms.