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The kinetics of grain growth in multicrystalline materials is determined by the interplay of curvature driven grain boundary motion and interfacial stress balance at the vertices of the grain boundaries. A comprehensive way to trent both effects in one model is given by the time dependet Ginzburg Landau model or phase field model. The paper presents the application of a multi phase field model recently developed for solidification processes to grain growth of a multicrystalline structure. The specific feature of this multi phase field model is its ability to treat each grain boundary with its individual characteristics dependent on the type of the grain boundary, its orientation or the local pinning at precipitates. The pinning effect is simulated on the nanometer scale resolving the interaction of an individual precipitate with a curved grain boundary. From these simulations an effective pinning force is deduced and a model of driving force dependent grain boundary mobility is formulated accounting for the pinning effect on the mesoscopic scale of the grain growth simulation. 2-D grain growth simulations are presented.