The solution procedure of coupled electromagnetic-/thermal-simulations with high resolution requires efficient solvers. High performance computing libraries and languages like Nvidia's CUDA help in unlocking the massively parallel capabilities of GPUs to accelerate calculations. They reduce the time needed to solve real world problems. In this paper, the speed-up is discussed, which is obtained by using GPUs for coupled time domain simulations with finite difference schemes. A tailor-made implementation of the time consuming sparse matrix vector multiplication is shown to have advantages over standard CUDA-libraries like cuSparse.