implementation of the parareal method for the heat equation on graphics processing units

The parareal algorithm is implemented on graphics processing units (gpu) using the cuda language. the algorithm, which enables parallel processing along the time coordinate, is used to solve the one-dimensional heat equation. the explicit and implicit euler schemes and also the crank-nicolson scheme are used for the time integration. furthermore, the central second-order finite difference scheme is utilized for discretizing the spatial derivative. the ordinary gpu implementation of the mentioned schemes are compared to that of the parareal implementation. the results show the parareal algorithm can achieve speedups of about 4.