Solution method of the Poisson equation for the electric field with a thin sheath Original Research Article

In the simulation of materials processing plasmas, one has to solve the Poisson equation for electric field at each electron timestep. This is a bottleneck for the numerical simulation of processing plasmas. In this paper, a drastically efficient method for solving the Poisson equation is proposed. In obtaining the solution, the variational principle is used together with the boundary-layer theory in fluid mechanics.