A Simplified Implicit Maxwell Solver

We apply the second-order formulation of Maxwellʹs equations proposed by Jiang et al. (1996, J. Comput. Phys.125, 104) to the solution of the implicit formulation of the three-dimensional, time-dependent Vlasov–Maxwellʹs system. An implicit finite difference algorithm is developed to solve the Maxwellʹs equations in a bounded domain with physical boundary conditions comprising electrically conducting walls (perfect conductors) and constant magnetic flux walls. We formulate the boundary conditions for Maxwellʹs equations to satisfy Poissonʹs equation throughout the domain by solving it only on the boundary. This eliminates the need for a separate projection step. We compare numerical results with analytical solutions for electromagnetic waves in vacuo, and using the implicit particle-in-cell code CELESTE3D, we test the new solver on the geospace environment modeling magnetic reconnection challenge problem.