  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 completely 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.
