A Multilevel Iterative Field Solver for Implicit Plasma Simulation Codes

Much e ort has gone into the development of implicit methods for electromagnetic kinetic plasma simulation. One such implicit method is the implicit moment method [1]. The maximum allowable time step in this method has often been found to be governed by the iterative elliptic eld solver, and not the implicit moment method itself [2]. In ref. [2] it was shown, in one dimension, that by using a direct method to solve the eld equations, signi cantly larger time steps could be achieved. We have initiated research into the development of an e cient and robust iterative elliptic solver which will allow similar time steps, and ne grid simulations, in two and three dimensions. Our algorithm uses the multigrid method [3] as a preconditioner to a Krylov subspace based iterative method, GMRES [4] in this work. Our goal is application of the proposed algorithm to three dimensional fully electromagnetic simulation. As a starting point we will work on the CELEST2D code, an unpublished modication of CELEST1D [2]. CELEST2D is electrostatic but contains a spatially varying (time independent) magnetic eld. Indeed, it is the electrostatic potential equation, from the implicit moment method, which provides the greatest challenge to iterative solvers. The elliptic equation for electrostatic potential, , in the implicit moment method of CELEST2D is,