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In electrodynamic field computations the continuous Maxwell equations are typically discretized in the space variables, i. e the continuous space is mapped onto a finite set of discrete elements leading to a system of differential equations constituting the Maxwell grid equations. These dynamical systems can be very large. Due to limited computational, accuracy and storage capabilities, simplified models, obtained by means of model order reduction (MOR) methods, which capture the main features of the original model are then successfully used instead of the original models. Most commonly MOR via projection is used. Variation of model parameters like geometrical or material parameters give rise to multivariate dynamical systems. It is aimed that also the simplified models keep this parameter dependence. In this work, MOR methods are presented for multivariate systems based on the finite integration technique (FIT). The methods are applied to numerical examples with both geometrical and material variations.