A semi-implicit electromagnetic FEM-PIC scheme with exact energy and charge conservation

Abstract

This article presents a new charge- and energy-conserving semi-implicit method (ChECSIM) for the Vlasov-Maxwell system. The Particle-in-Cell space discretization involves a structure-preserving Finite Element Method for the fields, and the time discretization is an adaptation of Lapenta's energy-conserving semi-implicit method (ECSIM) [33], which essentially consists of improving the latter with appropriate charge-conserving current deposition terms and an explicit correction step. As such, the resulting scheme is free of nonlinear iterations, and it preserves both energy and charge exactly.