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Numerical simulation of avalanches, saturated avalanches, and streamers can help us understand the detector physics of Resistive Plate Chambers (RPC). 3D Monte Carlo simulation of an avalanche inside an RPC, the transition from avalanche to saturated avalanche to streamer may help the search for the optimum voltage and alternate gas mixtures. This task is dauntingly resource-hungry, especially when space charge effects become important, which often coincides with important regimes of operation of these devices. By modifying the electric field inside the RPC dynamically, the space charge plays a crucial role in determining the response of the detector. In this work, a numerical model has been proposed to calculate the dynamic space-charge field inside an RPC and the same has been implemented in the Garfield++ framework. By modeling space charge as the large number of line charges and using the multithreading technique OpenMP to calculate electric field, drift line, electron gain, and space charge field, it has been possible to maintain time consumption within reasonable limits. For this purpose, a new class, pAvalancheMC has been introduced in Garfield++. The calculations have been successfully verified with those from existing solvers and an example is provided to show the performance of pAvalancheMC. Moreover, the details of the transition of an avalanche into a saturated avalanche have been discussed. The induced charge distribution is calculated for a timing RPC and results are verified with the experiment.