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Recently, the use of graphics processing units as a means of achieving the hardware acceleration of the finite-difference time-domain (FDTD) technique has attracted significant interest in the computational electromagnetics community. However, the large memory requirements of the FDTD, compounded by the limited memory resources available in graphics processing units, compromise the efficiency of this approach. Alternatively, the authors show how the implementation of the multiresolution time-domain technique in a graphics processing unit can optimally utilise the memory resources of the latter and achieve unprecedented acceleration rates, significantly higher than those achievable by the FDTD. A detailed description of the proposed implementation is provided, followed by rigorous numerical error and performance evaluation studies that conclusively verify the advantages of the graphics accelerated multiresolution time domain. Finally, the potential of this technique as a fast microwave wireless channel modelling tool is demonstrated.