Higher order finite elements in space and time for anisotropic simulations with variational integrators. Application of an efficient GPU implementation

In an implementation, however, the higher order approximation in space and time combined with the viscoelastic material suffers from a high computational effort. Hence, an efficient implementation is required in order to reduce the computational time to a minimum. In our approach, we face this problem by using a GPU and the programming architecture Cuda from NVIDIA, which allows a massive parallelization of time-consuming parts of the simulation. We introduce a pipeline design for the GPU implementation, which provides multiple advantages. This design allows a simple porting of an already existing implementation by means of self-managing pipeline-stages. However, a significant speedup is still achieved due to further optimizations which exploit the architecture of GPUs. In addition, when combining both hardware resources GPU and CPU the computational time can be reduced significantly once more. Therefore, our GPU implementation easily allows a distribution of computational effort between both GPU and CPU. Finally, we show in numerical examples the reached speedup of this approach, and the impact of combining the GPU and the CPU is studied in detail.