An Implicit, Asymptotic-Preserving and Energy-Charge-Conserving Method for the Vlasov-Maxwell System Near Quasi-Neutrality (Communications in Computational Physics, 2024)
An implicit, asymptotic-preserving and energy-charge-conserving (APECC)Particle-In-Cell (PIC) method is proposed to solve the Vlasov-Maxwell (VM) equations in the quasi-neutral regime. Charge conservation is enforced by particle orbitalaveraging and fixed sub-time steps. The truncation error depending on the number of sub-time steps is further analyzed. The temporal discretization is chosen bythe Crank-Nicolson method to conserve the discrete energy exactly. The key step inthe asymptotic-preserving iteration for the nonlinear system is based on a decomposition of the current density deduced from the Vlasov equation in the source of theMaxwell model. Moreover, we show that the convergence is independent of the quasi-neutral parameter. Extensive numerical experiments show that the proposed methodcan achieve asymptotic preservation and energy-charge conservation.