The simulation of Micro Pattern Gaseous Detectors (MPGDs) signal response is an important and powerful tool for the design and optimization of such detectors. However, several attempts to simulate exactly the effective charge gain have not been compl
etely successful. Namely, the gain stability over time has not been fully understood. Charging-up of the insulator surfaces have been pointed as one of the responsible for the difference between experimental and Monte Carlo results. This work describes two iterative methods to simulate the charging-up in one MPGD device, the Gas Electron Multiplier (GEM). The first method uses a constant step for avalanches time evolution, very detailed, but slower to compute. The second method uses a dynamic step that improves the computing time. Good agreement between both methods was reached. Despite of comparison with experimental results shows that charging-up plays an important role in detectors operation, should not be the only responsible for the difference between simulated and measured effective gain, but explains the time evolution in the effective gain.
