In this dissertation, we present a particle-in-cell method for the simulation of plasmas based on an unconditionally stable solver for the second-order scalar wave equation, that is, a wave equation solver that is not subject to a Courant-Friedrichs-Lewy (CFL) stability restriction, typical of explicit methods, while maintaining a computational cost and code complexity comparable to such explicit solvers. This permits the use of a time step size many times larger than allowed by widely-used explicit methods.
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