A Multilevel Iterative Field Solver for Implicit, Kinetic, Plasma Simulation

The equation for electrostatic potential which arises from the implicit moment method in plasma simulation is a nonsymmetric elliptic equation. We present results using a simple multigrid method as a preconditioner to General Minimum RESidual (GMRES) to iteratively solve this nonsymmetric elliptic equation in two dimensions. It is demonstrated that a simple multigrid method produces an effective preconditioner. It is also demonstrated that under some conditions the required number of linear iterations is independent of grid dimension. Results are presented for both uniform and nonuniform grid problems.

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