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The simulation of subtractive manufacturing processes has a long history in engineering. Corresponding predictions are utilized for planning, validation and optimization, e.g., of CNC-machining processes. With the up-rise of flexible robotic machining and the advancements of computational and algorithmic capability, the simulation of the coupled machine-process behaviour for complex machining processes and large workpieces is within reach. These simulations require fast material removal predictions and analysis with high spatial resolution for multi-axis operations. Within this contribution, we propose to leverage voxel-based concepts introduced in the computer graphics industry to accelerate material removal simulations. Corresponding schemes are well suited for massive parallelization. By leveraging the computational power offered by modern graphics hardware, the computational performance of high spatial accuracy volumetric voxel-based algorithms is further improved. They now allow for very fast and accurate volume removal simulation and analysis of machining processes. Within this paper, a detailed description of the data structures and algorithms is provided along a detailed benchmark for common machining operations. [ABSTRACT FROM AUTHOR]