With large-scale Integral Field Spectroscopy (IFS) surveys of thousands of galaxies currently under-way or planned, the astronomical community is in need of methods, techniques and tools that will allow the analysis of huge amounts of data. We focus on the kinematic modelling of disc galaxies and investigate the potential use of massively parallel architectures, such as the Graphics Processing Unit (GPU), as an accelerator for the computationally expensive model-fitting procedure. We review the algorithms involved in model-fitting and evaluate their suitability for GPU implementation. We employ different optimization techniques, including the Levenberg-Marquardt and Nested Sampling algorithms, but also a naive brute-force approach based on Nested Grids. We find that the GPU can accelerate the model-fitting procedure up to a factor of ~100 when compared to a single-threaded CPU, and up to a factor of ~10 when compared to a multi-threaded dual CPU configuration. Our method's accuracy, precision and robustness are assessed by successfully recovering the kinematic properties of simulated data, and also by verifying the kinematic modelling results of galaxies from the GHASP and DYNAMO surveys as found in the literature. The resulting GBKFIT code is available for download from: http://supercomputing.swin.edu.au/gbkfit.
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