Proposed here is a fast solution method for the Poisson equation in simulating the direct current (dc) and radio frequency (rf) discharges. The method is based on the variational method and the boundary-layer theory of fluid mechanics. The results obtained for one-dimensional discharges are in good agreement with those from the Particle-in-Cell/Monte Carlo (PIC/MC) method. The method can be applied not only to the particle model but also to the fluid model since the Poisson equation must be solved also in the latter model. (c) 2005 Elsevier B.V. All rights reserved.