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Developing particle-in-cell (PIC) methods using finite element basis sets,and without auxiliary divergence cleaning methods, was a long standing problemuntil recently. It was shown that if consistent spatial basis functions areused, one can indeed create a methodology that was charge conserving, albeitusing a leap-frog time stepping method. While this is a significant advance,leap frog schemes are only conditionally stable and time step sizes are closelytied to the underlying mesh. Ideally, to take full advantage of advances infinite element methods (FEMs), one needs a charge conserving PIC methodologythat is agnostic to the time stepping method. This is the principalcontribution of this paper. In what follows, we shall develop this methodology,prove that both charge and Gauss' laws are discretely satisfied at every timestep, provide the necessary details to implement this methodology for both thewave equation FEM and Maxwell Solver FEM, and finally demonstrate its efficacyon a suite of test problems. The method will be demonstrated by single particleevolution, non-neutral beams with space-charge, and adiabatic expansion of aneutral plasma, where the debye length has been resolved, and real mass ratiosare used.

Time Integrator Agnostic Charge Conserving Finite Element PIC