GPU-accelerated Exponential Time Difference Method for Parabolic Equations with Stiffness

Abstract

Abstract:In this work, we present a Graphics Processing Unit (GPU) accelerated Runge-Kutta exponential time difference (RKETD) method for parabolic equations with stiffness based on CUDA (Computed Unified Device Architecture). In the proposed method, the cuFFT library developed by NVIDIA is employed to compute discrete Fast Fourier Transforms (FFTs) which is the key part in the RKETD method on GPU. Several CUDA code optimization skills are used to improve the speedup performance. The comparison of the numerical results of CUDA-implemented RKETD method on GPU and original RKETD method on CPU demonstrates that the former can obtain good speedup performance. Numerical experiments demonstrate effectiveness and accuracy of the GPU acceleration for typical nonlinear parabolic problem with stiffness.