A GPU-based Fast Solution for Riesz Space Fractional Reaction-Diffusion Equation

The fast numerical solutions of Riesz fractional equation have computational cost of O(NMlogM), where M, N are the number of grid points and time steps. In this paper, we present a GPU-based fast solution for Riesz space fractional equation. The GPU-based fast solution, which is based on the fast method using FFT and implemented with CUDA programming model, consists of parallel FFT, vector-vector addition and vector-vector multiplication on GPU. The experimental results show that the GPU-based fast solution compares well with the exact solution. Compared to the known parallel fast solution on 8-core Intel E5-2670 CPU, the overall performance speedup on NVIDIA GTX650 GPU reaches 2.12 times and that on NVIDIA K20C GPU achieves 10.93 times.