Explicit relaxation Particle-in-Cell methods for Vlasov-Poisson equations with a strong magnetic field

Abstract

In this work, we present a novel family of explicit relaxation Particle-in-Cell (ER-PIC) methods for the Vlasov-Poisson equation with a strong magnetic field. These schemes achieve exact energy conservation by combining a splitting framework with the dynamic updating of a relaxation parameter at each time step. Using an averaging technique, we rigorously establish second-order error bounds for the Strang-type ER-PIC method and uniform first order accuracy in position for the Lie-Trotter ER-PIC scheme. Numerical experiments across the fluid, finite Larmor radius, and diffusion regimes confirm the accuracy and energy conservation of our methods.