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The simulation of Micro Pattern Gaseous Detectors (MPGDs) signal response isan important and powerful tool for the design and optimization of suchdetectors. However, several attempts to simulate exactly the effective chargegain have not been completely successful. Namely, the gain stability over timehas not been fully understood. Charging-up of the insulator surfaces have beenpointed as one of the responsible for the difference between experimental andMonte Carlo results. This work describes two iterative methods to simulate thecharging-up in one MPGD device, the Gas Electron Multiplier (GEM). The firstmethod uses a constant step for avalanches time evolution, very detailed, butslower to compute. The second method uses a dynamic step that improves thecomputing time. Good agreement between both methods was reached. Despite ofcomparison with experimental results shows that charging-up plays an importantrole in detectors operation, should not be the only responsible for thedifference between simulated and measured effective gain, but explains the timeevolution in the effective gain.

A dynamic method for charging-up calculations: the case of GEM