Diamond-Like Tiling Schemes for Efficient Explicit Euler on GPUs

GPU computing offers a high potential of raw processing power at comparatively low costs. This paper investigates optimization techniques for solving initial value problems (IVPs) of ordinary differential equations (ODEs) on GPUs. Different techniques, especially for exploiting the GPU memory hierarchy, are discussed, and corresponding OpenCL implementations of the explicit Euler method are compared using runtime experiments. The results show considerable performance improvements in many situations. Due to the basic character of the explicit Euler method, the results of this investigation can guide the optimization of more complex ODE methods with higher order and better stability on GPUs.