We present the simulation of the transient excitation and evolution of a TE34, 19 mode in the resonant cavity of the 170 GHz gyrotron. This gyrotron is planned for electron cyclotron resonance heating in the ITER tokamak fusion reactor. The numerical computation of a state-of-the-art gyrotron resonant cavity with a transient 3-D full wave particle-in-cell (PIC) method is a computationally demanding task. It was enabled by a highly scalable PIC scheme. To allow the numerical simulation of the high-frequency electromagnetic waves, we use a high-order discontinuous Galerkin method.