The equation for electrostatic potential which arises from the implicit mom
ent method in plasma simulation is a nonsymmetric elliptic equation. We pre
sent results using a simple multigrid method as a preconditioner to General
Minimum RESidual (GMRES) to iteratively solve this nonsymmetric elliptic e
quation in two dimensions. It is demonstrated that a simple multigrid metho
d 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. (C) 1999 Academic Press.