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Abstract. Ice sheets lose the majority of their mass through outlet glaciers or ice streams, corridors of fast ice moving multiple orders of magnitude more rapidly than the surrounding ice. The future stability of these corridors of fast-moving ice depends sensitively on the behaviour of their boundaries, namely shear margins, grounding zones and the basal sliding interface, where the stress field is complex and fundamentally three-dimensional. These boundaries are prone to thermomechanical localisation, which can be captured numerically only with high temporal and spatial resolution. Thus, better understanding the coupled physical processes that govern the response of these boundaries to climate change necessitates a non-linear, full Stokes model that affords high resolution and scales well in three dimensions. This paper's goal is to contribute to the growing toolbox for modelling thermomechanical deformation in ice by leveraging graphical processing unit (GPU) accelerators' parallel scalability. We propose FastICE, a numerical model that relies on pseudo-transient iterations to solve the implicit thermomechanical coupling between ice motion and temperature involving shear heating and a temperature-dependent ice viscosity. FastICE is based on the finite-difference discretisation, and we implement the pseudo-time integration in a matrix-free way. We benchmark the mechanical Stokes solver against the finite-element code Elmer/Ice and report good agreement among the results. We showcase a parallel version of FastICE to run on GPU-accelerated distributed memory machines, reaching a parallel efficiency of 99 %. We show that our model is particularly useful for improving our process-based understanding of flow localisation in the complex transition zones bounding rapidly moving ice.