The paper presents a novel approach for tracking the optimal grid size of the computational domain for modeling the corona problem within the wire-duct precipitators, which in turn helps in decreasing the experimental efforts. The Finite Difference Method (FDM) is used to model the corona problem using the full multi-grid method (FMG) as a powerful convergent iterative solution for Poisson equation particularly on finer computational domains. The full multi-grid method is examined against successive over relaxation (SOR) strategy and the latter is effectively transcendent in terms of timing performance. Indeed, using finer grids is a double ended weapon; on one hand it reduces the truncation error of the Finite Difference Method which reflects in getting more accurate view for the corona problem in precipitators. While on the other hand, the round offerror will be increased which might give un-accurate results. Accordingly, the issue of choosing the optimal grid size arises. The full multi-grid method tracked the optimal grid size that gives the appropriate results for the potential and current density that well matched the previous published experimental measurements.