The accurate simulation of excitonic energy transfer in molecular complexes with coupled electronic and vibrational degrees of freedom is essential for comparing excitonic systemparameters obtained from ab-initio methods with measured time-resolved spectra. Several exact methods for computing the exciton dynamics within a density-matrix formalism are known, * To whom correspondence should be addressed † Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany ‡ Mads Clausen Institute, University of Southern Denmark, Alsion 2, 6400 Sønderborg, Denmark ¶ Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford St, Cambridge, Massachusetts 02138, USA 1 but are restricted to small systems with less than ten sites due to their computational complexity. To study the excitonic energy transfer in larger systems, we adapt and extend the exact hierarchical equation of motion (HEOM) method to various high-performance many-core platforms using the Open Compute Language (OpenCL). For the light-harvesting complex II (LHC II) found in spinach, the HEOM results deviate from predictions of approximate theories and clarify the time-scale of the transfer-process. We investigate the impact of resonantly coupled vibrations on the relaxation and show that the transfer does not rely on a fine-tuning of specific modes.