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

This work studies a class of reduced relativistic Vlasov–Maxwell equations describing laser-plasma interaction. Fully discrete schemes are obtained by discretizing distribution functions using particle-in-cell methods, discretizing electromagnetic fields with compatible finite element methods in the framework of finite element exterior calculus in space, and discrete gradient methods combined with splitting methods in time. The proposed schemes are energy conserving and the discrete Poisson equations are also satisfied by the numerical solutions. Numerical experiments of parametric instability are conducted to validate the conservation properties and illustrate good long time behaviors of the numerical methods.