Despite economic uncertainties, engineering projects are constantly breaking barriers of scale, and in the quest for efficiency, sustainability and cost-effectiveness simulation is a fundamental element. Hybrid processing appears to be a strong candidate paradigm for reducing simulation time while improving the overall computing efficiency by employing dedicated accelerators to tackle specific problems. In several circumstances algorithms need re-thinking to exploit these new hybrid architectures: some methods that have traditionally been applied might not be applicable anymore, whereas other methods considered too expensive or impractical could be reconsidered, as hybrid systems can provide performance and efficiency benefits even in situations that are not apparent.