Patients who have suffered a myocardial infarction have an elevated risk of developing arrhythmia. The use of in silico experiments of the electrical activity in the hearts of these patients, is emerging as an alternative to traditional, more invasive in situ examinations. One of the principal barriers to the use of in silico experiments is the tremendous amount of computational power required to perform such simulations. Building on an existing code, we create a complete solver for the monodomain model, which describes the electrical activity in the heart. Through extensive optimisations, we manage to efficiently utilise an NVIDIA DGX-2 machine, which is currently the most powerful single-box general-purpose computer with its 16 V100 GPUs. With this solver, we achieve simulation speeds of 2 heartbeats per wall clock minute on the DGX-2 using a realistic unstructured tetrahedral mesh with 11.7 million cells, and we show that the achieved execution time using all 16 GPUs in the DGX-2 is only 30.2% higher than the theoretical lower bound.